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Photoelectric Effect Practice Paper 3: photon counts, quantum efficiency and graph gradients
Photoelectric Effect Practice Paper 3: photon counts, quantum efficiency and graph gradients
This paper treats light as a stream of particles: photons per second first, then electrons and current through the quantum efficiency, then Planck constant from the gradient of a stopping-voltage against frequency graph. The gradient is always h over e, and the intercept magnitude over e gives the work function. Every value is checked by computer.
Quick answer From 5.0e14 Hz the photon carries 2.07 eV; threshold 497 nm; a 4.0 eV photon against 2.5 eV leaves 1.5 eV; 1.5 V equals 2.4e-19 J; 250 nm against 4.0 eV leaves 0.97 eV; 0.60 mW; 0.16 mA; gradient 6.6e-34 with 2.0 eV; a rise of 1.04 eV; nothing below the threshold.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | 25 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: Photoelectric Effect |
| Level | S6 |
02 Questions (10 items)
- FoundationWhat is the energy in eV of a photon of frequency 5.0e14 Hz?
- FoundationWhat is the threshold wavelength of a metal with work function 2.5 eV?
- FoundationA 4.0 eV photon strikes a metal of work function 2.5 eV. What is the maximum kinetic energy?
- FoundationA stopping voltage of 1.5 V is found. What is the maximum kinetic energy in joules?
- IntermediateLight of 250 nm falls on a metal of work function 4.0 eV. What is the maximum kinetic energy?
- IntermediateA beam delivers 2.0e15 photons per second, each of energy 3.0e-19 J. What is the beam power?
- IntermediateA metal receives 5.0e15 photons per second with a quantum efficiency of 20%. What is the photocurrent?
- ChallengeThe stopping-voltage against frequency graph has a gradient of 6.6e-34 V s and an intercept of -2.0 V. Find h and the work function.
- ChallengeFor a metal of work function 2.0 eV the wavelength changes from 400 nm to 300 nm. By how much does the maximum kinetic energy rise?
- Error redoA student claims that a bright enough beam below the threshold frequency can still eject electrons. Where is the error?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3.32e-19 J, that is 2.07 eV. | E = hf = 6.63e-34 times 5.0e14 = 3.315e-19 J, then divide by 1.60e-19. |
| 2 | About 497 nm. | lambda0 = hc over W = 1.989e-25 divided by 4.00e-19 = 4.97e-7 m. |
| 3 | 1.5 eV, that is 2.4e-19 J. | Subtract directly: 4.0 minus 2.5 = 1.5 eV, then multiply by 1.60e-19 for joules. |
| 4 | 2.4e-19 J. | Kmax = e times Vs = 1.60e-19 times 1.5. |
| 5 | About 0.97 eV. | The photon carries 7.96e-19 J, that is 4.97 eV; subtract 4.0 eV. |
| 6 | 6.0e-4 W, that is 0.60 mW. | Power is photons per second times energy per photon = 2.0e15 times 3.0e-19. |
| 7 | 0.16 mA, that is 1.0e15 electrons per second. | Electrons per second = 0.20 times 5.0e15 = 1.0e15, multiplied by 1.60e-19 gives the current. |
| 8 | h = 6.6e-34 J s, the gradient times e; work function 2.0 eV, the intercept magnitude times e. | Vs = (h/e)f minus W/e, so the gradient times e is h and the intercept times e is W. |
| 9 | It rises by about 1.04 eV, from 1.11 eV to 2.14 eV. | The two photon energies are 3.11 eV and 4.14 eV; the difference is 1.04 eV and is independent of the work function. |
| 10 | An electron absorbs one photon only; below the threshold every photon carries less than the work function, so no electron can escape however many photons arrive. | The threshold is an energy condition, not a brightness one; this is the decisive break with the classical wave picture. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
