Photoelectric effect | PhysicsRank

A brighter beam supplies more light, but it need not eject electrons from a metal if each photon has too little energy. This separates two everyday ideas that often travel together: how much light arrives and how much energy each interaction can supply.

We follow a beam from photon energy and momentum through electron escape and stopping voltage, then compare the wavelengths of massive particles prepared at specified energies.

What you will learn to do

Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
Convert beam power to photon rate and a stated-efficiency current.
Relate photon momentum to absorption and reflection forces.
Apply the photoelectric threshold before computing a kinetic energy.
Interpret stopping voltage, its polarity and frequency slope.
Separate frequency effects from intensity and yield effects.
Use de Broglie wavelength with the correct massive-particle momentum model.
Apply accelerating-potential and simple matter-diffraction geometry.

Useful before this chapterFrom changing electric fields to electromagnetic waves →Interference, diffraction and the structure of a fringe pattern →

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

BEFORE YOU READ

Bring back one idea

Try a sentence or a sketch before opening the comparison. If this is new, use the explanation to get started.

At the same total optical power, must two beams of different frequencies contain the same number of photons per second?

Compare your reasoning

No. Each photon carries energy hf, so the higher-frequency beam needs fewer photons per second for the same power. Keep individual energy separate from the delivery rate.

Revisit the explanation →

01 / Photons, photoelectric emission and matter waves

Frequency sets the energy per photon

A photon of frequency ν carries energy Eγ = hν. In vacuum ν = c/λ0, so Eγ = hc/λ0. A shorter vacuum wavelength means a larger photon energy.

The energy per photon is different from the total beam power. Increasing the photon arrival rate at fixed frequency increases power without changing the energy of each photon. Changing frequency at fixed power changes how many photons arrive per second.

The electronvolt is an energy unit: 1 eV = 1.602 × 10⁻¹⁹ J to the precision used here. A charge of elementary-charge magnitude gains 1 eV of kinetic energy when accelerated through a 1 V potential difference under the appropriate conditions.

For optical calculations, hc ≈ 1240 eV·nm is convenient. Then dividing 1240 by a vacuum wavelength in nanometres gives photon energy in electronvolts. Use matching units and the constants specified by the problem.

A STORY BEHIND THE IDEA

Scattered light can return with a different frequency

C. V. Raman’s work showed that light scattered by molecules can contain components shifted in frequency from the incident light. Those shifted components carry information about the interaction with matter. Most of the scattered light need not undergo the same shift.

Using the photon model, a lower outgoing frequency means the photon has transferred energy to the material; a higher outgoing frequency means it has gained energy. This is a different process from ordinary refraction at a stationary interface, where the transmitted frequency stays fixed. Similar-looking light problems can therefore require different assumptions.

Carry this into the physicsAsk whether the process merely changes propagation or exchanges energy with matter before deciding which quantities remain fixed.

E_\gamma=h\nu=\frac{hc}{\lambda_0},\qquad E_\gamma(\mathrm{eV})\approx\frac{1240}{\lambda_0(\mathrm{nm})}

λ0 is vacuum wavelength. At a stationary material interface the frequency and photon energy remain the same even though the wavelength inside the medium changes.

WORKED EXAMPLE

Calculate one photon’s energy before discussing beam brightness

Find the photon energy for vacuum wavelength 400 nm using hc = 1240 eV·nm. Convert to joules using 1 eV = 1.602 × 10⁻¹⁹ J.

Choose an approach

Use the convenient optical energy-length constant, then convert the resulting energy unit.

Divide the energy-length product by the wavelength.
$E_\gamma=1240/400=3.10\ \mathrm{eV}$
Convert electronvolts to joules with the stated factor.
$E_\gamma=3.10(1.602\times10^{-19})=4.9662\times10^{-19}\ \mathrm J$

What this gives usEach photon carries approximately 3.10 eV, or 4.97 × 10⁻¹⁹ J.

Check the result another way

Doubling wavelength would halve this energy. Doubling beam power at the same wavelength would not change it.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Calculate one photon’s energy before discussing beam brightness
Problem: Find the photon energy for vacuum wavelength 400 nm using hc = 1240 eV·nm. Convert to joules using 1 eV = 1.602 × 10⁻¹⁹ J.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: Frequency sets the energy per photon
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
E_\gamma=h\nu=\frac{hc}{\lambda_0},\qquad E_\gamma(\mathrm{eV})\approx\frac{1240}{\lambda_0(\mathrm{nm})}
Meaning: λ0 is vacuum wavelength. At a stationary material interface the frequency and photon energy remain the same even though the wavelength inside the medium changes.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Back to chapter contents ↑

02 / Photons, photoelectric emission and matter waves

Power divided by photon energy gives the arrival rate

For a monochromatic beam, the photon rate is Ndot = P/Eγ. The numerator is energy per second and the denominator energy per photon, leaving photons per second. Over a duration t at constant power, the expected photon number is Pt/Eγ.

A detector or photoemitter need not register every incident photon. If an explicitly specified fraction η produces one collected electron per successful event, the mean collected current is eηNdot. This is a model with a stated quantum efficiency, not a universal one-electron-per-incident-photon rule.

At fixed monochromatic power, a larger photon energy means a smaller photon rate. At fixed photon rate, a larger energy means a larger power. Stating what is held fixed is essential when comparing two beams.

For a broad spectrum, different frequency components have different photon energies. A single central wavelength may not be enough to infer the total count accurately; sum or integrate the spectral power divided by hν.

WORKED EXAMPLE

Separate source power from detector efficiency

A monochromatic beam at 620 nm has power 0.64 mW. Use hc = 1240 eV·nm and e = 1.60 × 10⁻¹⁹ C for this estimate. A detector collects one electron for 10% of incident photons. Find photon rate and current.

Choose an approach

First calculate photon energy, then count photons and apply the stated efficiency.

Each 620 nm photon carries 2.0 eV.
$E_\gamma=1240/620=2.0\ \mathrm{eV}=3.20\times10^{-19}\ \mathrm J$
Divide the beam power by the individual photon energy.
$\dot N=\frac{0.64\times10^{-3}}{3.20\times10^{-19}}=2.0\times10^{15}\ \mathrm{s^{-1}}$
Only the stated successful fraction contributes a collected electron.
$I=e\eta\dot N=(1.60\times10^{-19})(0.10)(2.0\times10^{15})=32\ \mathrm{\mu A}$

What this gives usThe incident rate is 2.0 × 10¹⁵ photons/s and the mean collected current is 32 μA.

Check the result another way

Setting η = 1 would give 320 μA, so the stated 10% efficiency reduces the current by the expected factor ten.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Separate source power from detector efficiency
Problem: A monochromatic beam at 620 nm has power 0.64 mW. Use hc = 1240 eV·nm and e = 1.60 × 10⁻¹⁹ C for this estimate. A detector collects one electron for 10% of incident photons. Find photon rate and current.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: Power divided by photon energy gives the arrival rate
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

03 / Photons, photoelectric emission and matter waves

A massless photon still carries momentum

A photon in vacuum has zero rest mass but nonzero energy and momentum. Their relation is Eγ = pc, giving p = h/λ0. The nonrelativistic massive-particle expression p²/(2m) cannot be used for a photon.

Momentum is a vector along the photon propagation direction. Absorption transfers that momentum to the absorbing system. Reversal by ideal back reflection changes the photon momentum by twice its incident magnitude.

For a normally incident monochromatic beam absorbed completely, force equals photon rate times momentum: (P/Eγ)(Eγ/c) = P/c. Ideal back reflection gives 2P/c. This recovers the classical radiation-momentum result from a photon count.

Momentum assignment inside material media involves the field and the material together and requires a more careful system definition. The simple p = E/c relation in this section is explicitly for photons in vacuum.

p_\gamma=\frac{E_\gamma}{c}=\frac h{\lambda_0},\qquad F_{\mathrm{abs}}=\frac Pc,\qquad F_{\mathrm{back\ reflection}}=\frac{2P}{c}

Vacuum propagation, normal incidence and a stationary ideal absorbing or back-reflecting target.

WORKED EXAMPLE

Recover a beam force without knowing its colour

A 3.0 W beam in vacuum is completely absorbed at normal incidence. Find the force using c = 3.00 × 10⁸ m/s. What would ideal back reflection give?

Choose an approach

The photon rate and individual momentum combine to P/c.

Absorption transfers the incident momentum flux.
$F_{\mathrm{abs}}=3.0/(3.00\times10^8)=1.0\times10^{-8}\ \mathrm N$
Back reflection doubles the change of photon momentum.
$F_{\mathrm{refl}}=2.0\times10^{-8}\ \mathrm N$

What this gives usThe forces are 10 nN for absorption and 20 nN for ideal back reflection.

Check the result another way

At fixed power the vacuum momentum flux is independent of colour: fewer high-energy photons each carry more momentum.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Recover a beam force without knowing its colour
Problem: A 3.0 W beam in vacuum is completely absorbed at normal incidence. Find the force using c = 3.00 × 10⁸ m/s. What would ideal back reflection give?

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: A massless photon still carries momentum
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
p_\gamma=\frac{E_\gamma}{c}=\frac h{\lambda_0},\qquad F_{\mathrm{abs}}=\frac Pc,\qquad F_{\mathrm{back\ reflection}}=\frac{2P}{c}
Meaning: Vacuum propagation, normal incidence and a stationary ideal absorbing or back-reflecting target.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

04 / Photons, photoelectric emission and matter waves

Emission spends part of the photon energy on escape

In the elementary photoelectric model, an electron absorbs energy hν from one photon. Escaping from a material surface requires a minimum energy called the work function Φ. The largest emitted kinetic energy is Kmax = hν − Φ when this difference is nonnegative.

The work function depends on the material and surface condition. It is not the same as an isolated atom’s ionization energy. Electrons emitted from different initial states or after internal energy losses can have kinetic energies below the maximum.

The threshold frequency is ν0 = Φ/h, and the longest threshold vacuum wavelength is λ0,threshold = hc/Φ. For photon energies below Φ, the weak-field single-photon model predicts no photoemission, however large the count of those individually insufficient photons becomes.

This statement belongs to the specified single-photon regime. Multiphoton processes, strong-field effects, thermal emission and changing surface conditions are different mechanisms. The usual competitive-exam model neglects them unless the problem says otherwise.

K_{\max}=h\nu-\Phi,\qquad\nu_0=\Phi/h,\qquad\lambda_{\mathrm{threshold}}=hc/\Phi

Single-photon photoemission. Below threshold there are no emitted electrons in this model, rather than electrons with a negative kinetic energy.

WORKED EXAMPLE

Check the threshold before reporting an electron energy

A surface has work function 2.20 eV and is illuminated at vacuum wavelength 400 nm. Use hc = 1240 eV·nm. Find maximum electron kinetic energy and threshold wavelength.

Choose an approach

Compare the photon energy with the escape cost.

The photon energy exceeds the work function.
$E_\gamma=1240/400=3.10\ \mathrm{eV}>2.20\ \mathrm{eV}$
Subtract the work function for the maximum surplus energy.
$K_{\max}=3.10-2.20=0.90\ \mathrm{eV}$
Find the longest wavelength at the ideal threshold.
$\lambda_{\mathrm{threshold}}=1240/2.20\approx563.6\ \mathrm{nm}$

What this gives usThe maximum kinetic energy is 0.90 eV and threshold wavelength about 564 nm.

Check the result another way

A 700 nm photon would have only about 1.77 eV, below the work function, so the same single-photon model would predict no emission.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Check the threshold before reporting an electron energy
Problem: A surface has work function 2.20 eV and is illuminated at vacuum wavelength 400 nm. Use hc = 1240 eV·nm. Find maximum electron kinetic energy and threshold wavelength.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: Emission spends part of the photon energy on escape
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
K_{\max}=h\nu-\Phi,\qquad\nu_0=\Phi/h,\qquad\lambda_{\mathrm{threshold}}=hc/\Phi
Meaning: Single-photon photoemission. Below threshold there are no emitted electrons in this model, rather than electrons with a negative kinetic energy.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

05 / Photons, photoelectric emission and matter waves

A retarding voltage measures the fastest photoelectrons

In a photoelectric collector circuit, a suitable accelerating collector voltage gathers emitted electrons. Reversing the polarity can retard them: for electrons, a collector negative relative to the emitting surface raises the required potential-energy cost.

Increase the retarding voltage magnitude Vs until even the most energetic emitted electrons fail to reach the collector. The ideal stopping relation is eVs = Kmax, with e the positive elementary-charge magnitude and Vs a nonnegative retarding magnitude.

Numerically, an electron maximum kinetic energy of 0.90 eV corresponds to a stopping magnitude of 0.90 V. This convenient numerical equality is a unit conversion for one elementary charge, not an equality between volts and electronvolts as physical dimensions.

The stopping voltage measures the upper edge of the kinetic-energy distribution. It does not say every emitted electron has that energy. Contact potentials, stray fields and collection geometry can complicate actual measurements beyond the ideal model.

eV_s=K_{\max},\qquad V_s=\frac he\nu-\frac\Phi e

Vs is the magnitude of the voltage that retards emitted electrons; the collector is negative relative to the emitter in the simple setup.

WORKED EXAMPLE

Translate maximum electron energy into a retarding voltage

The previous surface emits electrons with Kmax = 0.90 eV. What stopping-voltage magnitude is needed, and which collector polarity retards the electrons?

Choose an approach

A retarding potential difference costs one electron an energy eVs.

Convert the energy condition using the definition of an electronvolt.
$eV_s=0.90\ \mathrm{eV}\quad\Rightarrow\quad V_s=0.90\ \mathrm V$
An electron’s potential energy rises toward a lower electric potential.
$\Delta U=q\Delta V=(-e)(-V_s)=+eV_s$

What this gives usA 0.90 V retarding magnitude is needed, with the collector negative relative to the emitter.

Check the result another way

The positive potential-energy increase removes kinetic energy, so the stated polarity is consistent with retardation.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Translate maximum electron energy into a retarding voltage
Problem: The previous surface emits electrons with Kmax = 0.90 eV. What stopping-voltage magnitude is needed, and which collector polarity retards the electrons?

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: A retarding voltage measures the fastest photoelectrons
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
eV_s=K_{\max},\qquad V_s=\frac he\nu-\frac\Phi e
Meaning: Vs is the magnitude of the voltage that retards emitted electrons; the collector is negative relative to the emitter in the simple setup.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

06 / Photons, photoelectric emission and matter waves

Frequency changes the stopping edge; intensity changes the available count

At fixed material work function, increasing frequency above threshold increases Kmax and the stopping-voltage magnitude linearly. The slope of Vs against ν is h/e, while the frequency-axis intercept is Φ/h.

At fixed frequency above threshold, increasing incident intensity increases the photon rate and can increase the saturation photocurrent when emission efficiency and collection conditions remain unchanged. It does not increase the ideal maximum energy per emitted electron.

A current–collector-voltage curve therefore carries two different kinds of information: the stopping edge concerns maximum kinetic energy, while the saturation level concerns collected electron rate. Mixing them leads to incorrect intensity-versus-frequency predictions.

At fixed beam power, changing frequency also changes photon count and may change quantum efficiency. Do not claim that saturation current is universally unchanged when frequency changes; identify the assumptions about source power and yield.

Read threshold and slope from a stopping-voltage graph

Inspect a plotted point: ν / (10¹⁴ Hz) = 5

Stopping edge: 0

Illustrative single-photon model with h/e = 4.14 × 10⁻¹⁵ V·s and work function 2.07 eV. The line starts at threshold; below it the model predicts no photoemission, not a negative electron kinetic energy. Lines connect the plotted samples.

WORKED EXAMPLE

Infer an energy scale from two stopping measurements

For one idealized surface, stopping magnitudes are 0.414 V at frequency 6.0 × 10¹⁴ Hz and 1.242 V at 8.0 × 10¹⁴ Hz. Find h/e from the slope and the work function in eV.

Choose an approach

Subtract the observations to remove the material intercept.

The slope is voltage change divided by frequency change.
$\frac he=\frac{1.242-0.414}{(8.0-6.0)\times10^{14}}=4.14\times10^{-15}\ \mathrm{V\,s}$
Recover the intercept from either observation.
$\frac\Phi e=(4.14\times10^{-15})(6.0\times10^{14})-0.414=2.07\ \mathrm V$

What this gives usThe inferred slope is 4.14 × 10⁻¹⁵ V·s and work function 2.07 eV.

Check the result another way

The threshold frequency is 2.07/(4.14 × 10⁻¹⁵) = 5.0 × 10¹⁴ Hz, agreeing with the graph’s intercept.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Infer an energy scale from two stopping measurements
Problem: For one idealized surface, stopping magnitudes are 0.414 V at frequency 6.0 × 10¹⁴ Hz and 1.242 V at 8.0 × 10¹⁴ Hz. Find h/e from the slope and the work function in eV.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: Frequency changes the stopping edge; intensity changes the available count
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

07 / Photons, photoelectric emission and matter waves

An X-ray tube has a continuum edge and atomic lines

An electron accelerated toward a target gains kinetic energy from the voltage. When its motion is deflected or slowed by the target’s electric fields, it can emit bremsstrahlung photons with a range of energies. One photon cannot take more than the electron’s available kinetic energy in the ideal endpoint model.

The upper photon-energy bound becomes a lower wavelength bound because Eγ = hc/λ. Starting from negligible initial kinetic energy gives Eγ,max = eV and λmin = hc/(eV). This is a conservation-of-energy endpoint, not a statement that every incident electron produces one photon at the endpoint.

Sharper characteristic lines have a different origin: an electron fills a vacancy in an inner atomic shell, and the energy difference can leave as a photon. Their energies depend on the target atom’s level structure. Raising tube voltage can enable a previously inaccessible excitation and change intensity; it does not continuously shift a fixed atomic transition energy in this basic model.

Do not confuse generating an inner-shell vacancy with emitting a characteristic photon. The excitation threshold must be met first, and relaxation may also transfer energy to another electron. A continuum spectrum and characteristic lines can therefore occur together without sharing the same wavelength-setting mechanism.

E_{\gamma,\max}=eV,\qquad\lambda_{\min}=\frac{hc}{eV}

V is the positive accelerating-voltage magnitude. e is the elementary charge magnitude. Use vacuum wavelength; if eV is expressed in electronvolts, use hc in matching energy–length units.

WORKED EXAMPLE

Compare an energy bound with a possible line

A tube accelerates electrons through 20 kV. Use hc = 1240 eV·nm. Find its ideal continuum cutoff, then compare it with a hypothetical characteristic photon of energy 12 keV, assuming the relevant vacancy can be produced.

Choose an approach

Compute the endpoint and the line from their separate energy scales.

The largest available single-photon energy is 20,000 eV.
$\lambda_{\min}=1240/20000=0.0620\ \mathrm{nm}$
The line’s energy is set by its atomic transition.
$\lambda_{\mathrm{line}}=1240/12000\approx0.1033\ \mathrm{nm}$

What this gives usThe line lies at a longer wavelength than the cutoff, consistent with its lower photon energy. Energy availability alone does not establish the vacancy-production probability.

Check the result another way

A 0.031 nm photon would require 40 keV, exceeding the stated electron energy.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Compare an energy bound with a possible line
Problem: A tube accelerates electrons through 20 kV. Use hc = 1240 eV·nm. Find its ideal continuum cutoff, then compare it with a hypothetical characteristic photon of energy 12 keV, assuming the relevant vacancy can be produced.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

STOP & THINK

At the same voltage, changing the target material can change characteristic line positions. Must it change the ideal continuum cutoff too?

YesNo

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves / An X-ray tube has a continuum edge and atomic lines
Problem: At the same voltage, changing the target material can change characteristic line positions. Must it change the ideal continuum cutoff too?
Choices:
1. Yes
2. No

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: An X-ray tube has a continuum edge and atomic lines
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
E_{\gamma,\max}=eV,\qquad\lambda_{\min}=\frac{hc}{eV}
Meaning: V is the positive accelerating-voltage magnitude. e is the elementary charge magnitude. Use vacuum wavelength; if eV is expressed in electronvolts, use hc in matching energy–length units.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

08 / Photons, photoelectric emission and matter waves

Matter-wave wavelength is determined by momentum

Particles with nonzero rest mass also display interference and diffraction. Their de Broglie wavelength is λ = h/p, where p is the momentum magnitude. The wave describes quantum probability amplitudes; it is not a claim that an electron is a tiny classical object physically wobbling through a sinusoidal path.

For nonrelativistic motion, p = mv and K = p²/(2m). Thus λ = h/√(2mK). At equal momentum, different particles have equal de Broglie wavelengths. At equal kinetic energy, their wavelengths scale as 1/√m in this approximation.

Do not use the photon relation E = pc for the kinetic energy of a slow massive particle. The general relation is Etotal² = p²c² + m²c⁴, with Etotal = K + mc². The nonrelativistic formula follows only when K is small compared with mc².

For macroscopic objects at ordinary speeds, momentum is large compared with atomic-scale values, so the de Broglie wavelength is extremely small. The relation still identifies a wave scale, but observing coherent interference also requires suitable preparation and isolation.

\lambda=\frac hp,\qquad\lambda_{\mathrm{nonrel}}=\frac h{\sqrt{2mK}}

The de Broglie relation uses momentum. The second expression additionally assumes nonrelativistic kinetic energy.

WORKED EXAMPLE

State what is equal before comparing two particles

Two nonrelativistic particles have the same kinetic energy, and the second has four times the mass of the first. Compare their de Broglie wavelengths.

Choose an approach

At fixed kinetic energy, momentum scales with the square root of mass.

The momentum ratio follows from p = √(2mK).
$p_2/p_1=\sqrt{m_2/m_1}=2$
Wavelength is inversely proportional to momentum.
$\lambda_2/\lambda_1=p_1/p_2=1/2$

What this gives usThe heavier particle has half the wavelength at equal nonrelativistic kinetic energy.

Check the result another way

At equal speed instead, its momentum would be four times larger and wavelength one quarter. The preparation condition changes the comparison.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: State what is equal before comparing two particles
Problem: Two nonrelativistic particles have the same kinetic energy, and the second has four times the mass of the first. Compare their de Broglie wavelengths.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: Matter-wave wavelength is determined by momentum
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
\lambda=\frac hp,\qquad\lambda_{\mathrm{nonrel}}=\frac h{\sqrt{2mK}}
Meaning: The de Broglie relation uses momentum. The second expression additionally assumes nonrelativistic kinetic energy.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

09 / Photons, photoelectric emission and matter waves

An accelerating voltage fixes kinetic energy, then wavelength

A particle of charge magnitude |q| accelerated from rest through a potential difference that increases its kinetic energy by |q|V has K = |q|V if other losses are negligible. Combining this with the nonrelativistic momentum relation gives λ = h/√(2m|q|V).

The wavelength scales as V⁻¹/². Quadrupling accelerating voltage halves wavelength; doubling voltage reduces it by √2. A direct inverse-voltage rule would be wrong.

For an electron accelerated through a modest voltage, substituting constants gives λ approximately 1.226 nm/√(V in volts). The numerical coefficient includes the electron mass and charge and should not be reused for protons or multiply charged ions.

Check the nonrelativistic condition using the particle’s rest-energy scale. For electrons, mc² is about 511 keV. At kinetic energies that are a substantial fraction of that scale, use relativistic momentum rather than extending the square-root formula uncritically.

\lambda=\frac h{\sqrt{2m|q|V}}\quad\text{from rest, nonrelativistic},\qquad pc=\sqrt{K(K+2mc^2)}\quad\text{relativistically}

The acceleration direction must produce a positive kinetic-energy gain. The relativistic expression follows from the total-energy relation.

WORKED EXAMPLE

Calculate an electron wavelength and verify the regime

An electron accelerates from rest through 100 V with negligible losses. Use λ ≈ 1.226 nm/√(V in volts). Find its wavelength and check whether the nonrelativistic approximation is appropriate.

Choose an approach

The kinetic energy is 100 eV, far below the electron rest energy.

Apply the electron-specific numerical relation.
$\lambda\approx\frac{1.226}{\sqrt{100}}\ \mathrm{nm}=0.1226\ \mathrm{nm}$
Compare the kinetic energy with the rest-energy scale.
$K/(mc^2)\approx100/511000\approx1.96\times10^{-4}$

What this gives usThe wavelength is approximately 0.123 nm, and the nonrelativistic approximation is appropriate for this estimate.

Check the result another way

Increasing the accelerating voltage to 400 V would halve the wavelength to about 0.0613 nm under the same approximation.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Calculate an electron wavelength and verify the regime
Problem: An electron accelerates from rest through 100 V with negligible losses. Use λ ≈ 1.226 nm/√(V in volts). Find its wavelength and check whether the nonrelativistic approximation is appropriate.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: An accelerating voltage fixes kinetic energy, then wavelength
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
\lambda=\frac h{\sqrt{2m|q|V}}\quad\text{from rest, nonrelativistic},\qquad pc=\sqrt{K(K+2mc^2)}\quad\text{relativistically}
Meaning: The acceleration direction must produce a positive kinetic-energy gain. The relativistic expression follows from the total-energy relation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

10 / Photons, photoelectric emission and matter waves

Interference measures a wave scale without assigning a classical path

An electron beam with sufficiently well-defined momentum can diffract from a suitable aperture or crystal. The locations of interference features depend on its de Broglie wavelength, just as optical phase differences depend on wavelength.

For coherent matter waves through two slits in the far-field small-angle regime, the same geometrical phase argument gives spacing λD/d. The detection events are localized, but many events can build a distribution with interference fringes.

A crystal has regularly spaced scattering planes. In the simple elastic-scattering geometry, constructive Bragg directions satisfy 2d sin θ = mλ, with θ measured from the lattice planes, not their normal. This angle convention differs from the incidence convention in elementary refraction.

The wavelength relation predicts feature locations; the actual scattering strengths, coherence and detector response require additional physics. One should not infer a definite unobserved classical trajectory through the apparatus from the final interference pattern alone.

WORKED EXAMPLE

Use the plane angle in a crystal-spacing calculation

Matter waves of wavelength 0.10 nm scatter elastically from planes separated by 0.20 nm. Find the first-order Bragg angle measured from the planes.

Choose an approach

Use the round-trip path difference between adjacent planes.

At first order, the path difference equals one wavelength.
$2d\sin\theta=\lambda\quad\Rightarrow\quad\sin\theta=0.10/(2\times0.20)=0.25$
Take the inverse sine with the stated plane-based convention.
$\theta\approx14.48^\circ$

What this gives usThe first-order angle is about 14.5° from the lattice planes.

Check the result another way

The scattering angle between incident and reflected directions is 2θ in this simple geometry; confusing it with θ would double the reported angle.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Worked-example topic: Use the plane angle in a crystal-spacing calculation
Problem: Matter waves of wavelength 0.10 nm scatter elastically from planes separated by 0.20 nm. Find the first-order Bragg angle measured from the planes.

Guide me through reconstructing the argument myself. Ask why each step is justified before moving to the next.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Focus: Interference measures a wave scale without assigning a classical path
Learning goals:
- Calculate photon energy in joules or electronvolts with explicit vacuum wavelength.
- Convert beam power to photon rate and a stated-efficiency current.
- Relate photon momentum to absorption and reflection forces.
- Apply the photoelectric threshold before computing a kinetic energy.
- Interpret stopping voltage, its polarity and frequency slope.
- Separate frequency effects from intensity and yield effects.
- Use de Broglie wavelength with the correct massive-particle momentum model.
- Apply accelerating-potential and simple matter-diffraction geometry.
Equations in this section (LaTeX):
Build the physical reasoning before choosing an equation.

Start by checking the prerequisite idea I need most. Use a simple example, then change one condition to test my understanding.

Back to chapter contents ↑

BRING THE IDEAS TOGETHER

What should stay with you

Frequency sets individual photon energy; beam power also depends on photon rate.
Vacuum photons obey E = pc and carry momentum despite zero rest mass.
The work function is an escape energy for a surface, not an isolated-atom ionization energy.
Below threshold the elementary photoelectric model predicts no emission, not negative kinetic energy.
Stopping voltage measures the fastest emitted electrons; saturation current concerns collected event rate.
Matter wavelength is h/p; p = √(2mK) is a nonrelativistic specialization.
A voltage or mass comparison must state what is held fixed.
Interference geometry applies to coherent matter amplitudes without supplying a classical hidden trajectory.

RETRIEVE, THEN EXPLAIN

Try it without the examples

Work these out before checking. If an answer surprises you, identify which assumption or step needs another look. A correct choice is most useful when you can explain why the alternatives fail.

SELF CHECK 1

Using hc = 1240 eV·nm, what photon energy corresponds to vacuum wavelength 620 nm?

Your answer (eV)Use a decimal, a fraction such as 1/3, or scientific notation.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: Using hc = 1240 eV·nm, what photon energy corresponds to vacuum wavelength 620 nm?
Requested answer unit: eV

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

SELF CHECK 2

A 4.0 eV photon acts on a surface of work function 2.5 eV in the single-photon model. What stopping-voltage magnitude follows?

Your answer (V)Use a decimal, a fraction such as 1/3, or scientific notation.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: A 4.0 eV photon acts on a surface of work function 2.5 eV in the single-photon model. What stopping-voltage magnitude follows?
Requested answer unit: V

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

SELF CHECK 3

Using hc = 1240 eV·nm, what threshold wavelength belongs to work function 3.10 eV?

Your answer (nm)Use a decimal, a fraction such as 1/3, or scientific notation.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: Using hc = 1240 eV·nm, what threshold wavelength belongs to work function 3.10 eV?
Requested answer unit: nm

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

SELF CHECK 4

A nonrelativistic particle accelerates from rest through a voltage four times larger, with the same mass and charge. What is the new-to-old wavelength ratio?

Your answerUse a decimal, a fraction such as 1/3, or scientific notation.

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: A nonrelativistic particle accelerates from rest through a voltage four times larger, with the same mass and charge. What is the new-to-old wavelength ratio?
Requested answer unit: 

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

SELF CHECK 5

At fixed above-threshold frequency and unchanged surface conditions, a larger weak-field light intensity changes the ideal photoelectric maximum energy how?

It increases linearly with intensityIt stays fixed, although the available electron rate can increaseIt becomes negative

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: At fixed above-threshold frequency and unchanged surface conditions, a larger weak-field light intensity changes the ideal photoelectric maximum energy how?
Choices:
1. It increases linearly with intensity
2. It stays fixed, although the available electron rate can increase
3. It becomes negative

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

SELF CHECK 6

Two particles have the same momentum magnitude. Their de Broglie wavelengths are:

EqualLarger for the heavier particle automaticallyDetermined only by their charges

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: Two particles have the same momentum magnitude. Their de Broglie wavelengths are:
Choices:
1. Equal
2. Larger for the heavier particle automatically
3. Determined only by their charges

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

SELF CHECK 7

A photon’s energy is below a surface work function in the weak single-photon model. What should a solution report?

A negative emitted kinetic energyNo photoemission by that mechanismEmission after enough waiting in every case

Study with a tutor prompt

Copy this into your AI assistant, then describe where you got stuck. It asks the tutor to coach you one step at a time. Check its reasoning against the lesson.

Topic: Photons, photoelectric emission and matter waves
Problem: A photon’s energy is below a surface work function in the weak single-photon model. What should a solution report?
Choices:
1. A negative emitted kinetic energy
2. No photoemission by that mechanism
3. Emission after enough waiting in every case

Help me choose a model and explain my reasoning before checking my answer.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.

APPLY THE CHAPTER

Take the ideas into a problem

Try a complete problem next. Commit to a method before revealing a hint, then compare your reasoning with the worked solution.

COME BACK TO THE IDEA

What can you explain later?

Try these from memory at your next study session, then again a few days later. Say your reasoning aloud or sketch it before looking. Adjust the gap to what you can explain.

Next study session

Within the single-photon photoelectric model, what changes when intensity increases at fixed frequency above threshold?

Compare your reasoning

More photons can produce more emitted electrons per second under unchanged collection conditions. The maximum photoelectron kinetic energy is still set by hf minus the work function, not by intensity alone.

Revisit the explanation →

A few days later: change the situation

What changes when tube voltage increases, and what changes when the X-ray target atom changes?

Compare your reasoning

Voltage changes the electron-energy bound and therefore the ideal continuum cutoff. Target atomic energy gaps set characteristic line energies. Excitation thresholds and intensities still need their own conditions.

Revisit the explanation →

Compare the physical reason, the assumptions and the conclusion. Your wording can differ. If one part is missing, revisit that section and try explaining it again after a break.

Back to chapter contents ↑