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A Level H2 Physics Modern Physics Quiz

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Questions

A-Level Physics H2 Quiz - Modern Physics

Name: __________________________
Class: __________________________
Date: __________________________
Score: ________ / 45

Duration: 60 minutes
Total Marks: 45

Instructions:

Answer all questions.
Write your answers in the spaces provided.
The number of marks is given in brackets [ ] at the end of each question or part question.
You may use a scientific calculator.
Assume the speed of light in vacuum $c = 3.00 \times 10^8 \text{ m s}^{-1}$ , Planck constant $h = 6.63 \times 10^{-34} \text{ J s}$ , and elementary charge $e = 1.60 \times 10^{-19} \text{ C}$ unless otherwise stated.

Section A: Photoelectric Effect and Quantum Nature of Light

1. State the meaning of the work function of a metal.
[1]

2. In a photoelectric effect experiment, ultraviolet radiation of wavelength 250 nm is incident on a clean zinc surface. The work function of zinc is $4.3 \text{ eV}$ .
Calculate the maximum kinetic energy of the emitted photoelectrons in joules.
[3]

3. The intensity of the incident radiation in Question 2 is doubled while keeping the wavelength constant.
State and explain the effect, if any, on:
(a) the maximum kinetic energy of the photoelectrons,
[2]

(b) the photoelectric current.
[2]

4. Explain why the existence of a threshold frequency for photoelectric emission supports the particle nature of light rather than the wave nature.
[3]

5. A student plots a graph of stopping potential $V_s$ against frequency $f$ of incident radiation for a specific metal surface.
(a) State the significance of the gradient of this graph.
[1]

(b) State the significance of the intercept on the frequency axis.
[1]

Section B: Atomic Spectra and Energy Levels

6. Define the term ionisation energy of an atom.
[1]

7. The diagram below shows three energy levels of a hydrogen atom:
$E_3 = -1.51 \text{ eV}$
$E_2 = -3.40 \text{ eV}$
$E_1 = -13.6 \text{ eV}$

Calculate the wavelength of the photon emitted when an electron transitions from level $E_3$ to level $E_2$ .
[3]

8. Explain why atomic emission spectra consist of discrete lines rather than a continuous spectrum.
[2]

9. An electron with kinetic energy 12.0 eV collides with a hydrogen atom in its ground state ( $E_1 = -13.6 \text{ eV}$ ). The first excited state is at $E_2 = -3.40 \text{ eV}$ .
(a) Determine whether this collision can excite the hydrogen atom to the $n=2$ level. Show your working.
[2]

(b) State what happens to the remaining kinetic energy of the incident electron if excitation occurs.
[1]

10. Describe the production of characteristic X-rays in an X-ray tube.
[3]

Section C: Nuclear Physics and Radioactivity

11. Define the term binding energy of a nucleus.
[2]

12. Calculate the binding energy per nucleon (in MeV) for a Helium-4 nucleus ( $^4_2\text{He}$ ).
Given:
Mass of proton = $1.00728 \text{ u}$
Mass of neutron = $1.00867 \text{ u}$
Mass of $^4_2\text{He}$ nucleus = $4.00151 \text{ u}$
$1 \text{ u} = 931.5 \text{ MeV}$
[3]

13. State two differences between $\beta^-$ decay and $\gamma$ emission.
[2]

14. A radioactive source has a half-life of 15 hours. The initial activity is $8.0 \times 10^4 \text{ Bq}$ .
Calculate the activity of the source after 60 hours.
[2]

15. Explain why the mass of a stable nucleus is less than the sum of the masses of its constituent protons and neutrons.
[2]

16. The graph below shows the variation of binding energy per nucleon with nucleon number $A$ .
(Imagine a standard curve peaking at Fe-56)
(a) State the approximate nucleon number $A$ where the binding energy per nucleon is maximum.
[1]

(b) Use the concept of binding energy per nucleon to explain why energy is released during nuclear fusion of light nuclei.
[3]

Section D: Wave-Particle Duality and Applications

17. Calculate the de Broglie wavelength of an electron accelerated through a potential difference of 150 V.
(Mass of electron $m_e = 9.11 \times 10^{-31} \text{ kg}$ )
[3]

18. In an electron diffraction experiment, electrons are fired at a thin graphite crystal. A ring pattern is observed on the screen.
(a) What property of electrons does this experiment demonstrate?
[1]

(b) State and explain the effect on the diameter of the rings if the accelerating voltage is increased.
[2]

19. A laser emits light of wavelength 633 nm with a power of 2.0 mW.
Calculate the number of photons emitted by the laser per second.
[3]

20. Explain the principle of stimulated emission and state one condition required for it to occur in a laser medium.
[3]

End of Quiz

Answers

A-Level Physics H2 Quiz - Modern Physics (Answer Key)

1. The minimum energy required to remove an electron from the surface of a metal. [1]

2.
Energy of incident photon $E = \frac{hc}{\lambda}$
$E = \frac{6.63 \times 10^{-34} \times 3.00 \times 10^8}{250 \times 10^{-9}} = 7.956 \times 10^{-19} \text{ J}$ [1]
Work function $\Phi = 4.3 \text{ eV} = 4.3 \times 1.60 \times 10^{-19} = 6.88 \times 10^{-19} \text{ J}$ [1]
Max KE $= E - \Phi = 7.956 \times 10^{-19} - 6.88 \times 10^{-19} = 1.076 \times 10^{-19} \text{ J}$
Answer: $1.1 \times 10^{-19} \text{ J}$ [1]

3.
(a) No change. [1]
Max KE depends only on the frequency (energy) of individual photons and the work function ( $KE_{max} = hf - \Phi$ ). Intensity does not change photon energy. [1]
(b) Increases. [1]
Intensity is proportional to the number of photons incident per unit time. More photons cause more photoelectrons to be emitted per second, increasing the current. [1]

4.
Wave theory predicts that energy accumulates over time, so emission should occur at any frequency given enough intensity/time. [1]
Particle theory states energy is quantized in packets ( $E=hf$ ). [1]
If $hf < \Phi$ , no single photon has enough energy to eject an electron, regardless of intensity. This explains the threshold frequency. [1]

5.
(a) Planck constant $h$ (or $h/e$ if plotting $V_s$ vs $f$ , since $eV_s = hf - \Phi \Rightarrow V_s = \frac{h}{e}f - \frac{\Phi}{e}$ ). Note: Standard syllabus accepts $h/e$ for gradient of $V_s$ vs $f$ . [1]
(b) Threshold frequency $f_0$ . [1]

6. The minimum energy required to remove an electron from the ground state of an atom to infinity (where it is free from the nucleus). [1]

7.
Energy difference $\Delta E = E_3 - E_2 = -1.51 - (-3.40) = 1.89 \text{ eV}$ [1]
Convert to Joules: $1.89 \times 1.60 \times 10^{-19} = 3.024 \times 10^{-19} \text{ J}$
$\lambda = \frac{hc}{\Delta E} = \frac{6.63 \times 10^{-34} \times 3.00 \times 10^8}{3.024 \times 10^{-19}}$ [1]
$\lambda = 6.59 \times 10^{-7} \text{ m}$ (or 659 nm) [1]

8.
Electrons in atoms occupy discrete/quantized energy levels. [1]
Transitions occur only between these specific levels, emitting photons of specific energies (and thus specific wavelengths/frequencies). [1]

9.
(a) Energy required for transition $n=1 \to n=2$ :
$\Delta E = E_2 - E_1 = -3.40 - (-13.6) = 10.2 \text{ eV}$ [1]
Since incident electron KE (12.0 eV) > 10.2 eV, excitation can occur. [1]
(b) The remaining kinetic energy ( $12.0 - 10.2 = 1.8 \text{ eV}$ ) is retained by the incident electron as kinetic energy. [1]

10.
High-speed electrons from the cathode collide with target atoms. [1]
They knock out inner-shell (e.g., K-shell) electrons, creating a vacancy. [1]
Outer-shell electrons drop down to fill the vacancy, emitting X-ray photons with specific energies corresponding to the difference in binding energies of the shells. [1]

11.
The energy required to completely separate a nucleus into its constituent protons and neutrons. [1]
(Or: The energy released when protons and neutrons combine to form a nucleus). [1]

12.
Mass of constituents: $2(1.00728) + 2(1.00867) = 2.01456 + 2.01734 = 4.03190 \text{ u}$ [1]
Mass defect $\Delta m = 4.03190 - 4.00151 = 0.03039 \text{ u}$
Binding Energy $BE = 0.03039 \times 931.5 = 28.308 \text{ MeV}$ [1]
BE per nucleon $= 28.308 / 4 = 7.08 \text{ MeV}$ [1]

13.

$\beta^-$ involves emission of an electron (and antineutrino); $\gamma$ is electromagnetic radiation (photon). [1]
$\beta^-$ changes the proton/neutron number (transmutation); $\gamma$ does not change the composition of the nucleus. [1]
(Other valid answers: Charge, Mass, Penetrating power)

14.
Number of half-lives $n = 60 / 15 = 4$ [1]
Activity $A = A_0 (1/2)^n = 8.0 \times 10^4 \times (1/2)^4$
$A = 8.0 \times 10^4 / 16 = 5.0 \times 10^3 \text{ Bq}$ [1]

15.
When nucleons combine, energy is released (binding energy). [1]
By mass-energy equivalence ( $E=mc^2$ ), this loss of energy corresponds to a loss of mass. [1]

16.
(a) $A \approx 56$ (Iron/Fe). [1]
(b) Light nuclei have lower BE per nucleon than the product nucleus formed after fusion. [1]
The product nucleus is more tightly bound (higher BE per nucleon). [1]
The increase in total binding energy corresponds to energy released to the surroundings. [1]

17.
Kinetic Energy $KE = eV = 1.60 \times 10^{-19} \times 150 = 2.40 \times 10^{-17} \text{ J}$
Momentum $p = \sqrt{2m_e KE} = \sqrt{2 \times 9.11 \times 10^{-31} \times 2.40 \times 10^{-17}}$ [1]
$p = \sqrt{4.3728 \times 10^{-47}} = 6.61 \times 10^{-24} \text{ kg m s}^{-1}$
$\lambda = h/p = \frac{6.63 \times 10^{-34}}{6.61 \times 10^{-24}}$ [1]
$\lambda = 1.00 \times 10^{-10} \text{ m}$ [1]

18.
(a) Wave nature (or wave-particle duality). [1]
(b) Diameter decreases. [1]
Higher voltage $\rightarrow$ higher momentum $\rightarrow$ shorter de Broglie wavelength. Shorter wavelength diffracts less, resulting in smaller ring diameters. [1]

19.
Energy of one photon $E = \frac{hc}{\lambda} = \frac{6.63 \times 10^{-34} \times 3.00 \times 10^8}{633 \times 10^{-9}} = 3.14 \times 10^{-19} \text{ J}$ [1]
Power $P = 2.0 \text{ mW} = 2.0 \times 10^{-3} \text{ J s}^{-1}$
Number of photons $N = \frac{P}{E} = \frac{2.0 \times 10^{-3}}{3.14 \times 10^{-19}}$ [1]
$N = 6.37 \times 10^{15} \text{ s}^{-1}$ [1]

20.
An incident photon of specific energy interacts with an excited atom, causing it to drop to a lower energy level and emit a second photon. [1]
The emitted photon is identical to the incident photon in frequency, phase, direction, and polarization. [1]
Condition: Population Inversion (more atoms in excited state than ground state). [1]

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