A Level H2 Physics Modern Physics Quiz

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A-Level Physics H2 Quiz - Modern Physics

Name: ____________________ Class: ____________________ Date: ____________________ Score: / 60

Duration: 90 Minutes
Total Marks: 60
Instructions: Answer all questions. Show all working for calculations. Use $h = 6.63 \times 10^{-34}\text{ J s}$, $c = 3.00 \times 10^8\text{ m s}^{-1}$, $e = 1.60 \times 10^{-19}\text{ C}$, and $1\text{ u} = 1.66 \times 10^{-27}\text{ kg}$.

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Section A: Quantum Physics (Questions 1–7)

1. State the photoelectric equation and define each term used. [3]
   
   
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2. A metal surface has a work function of $2.3\text{ eV}$. Calculate the threshold frequency of radiation required to eject electrons from the surface. [3]
   
   
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3. Radiation of wavelength $300\text{ nm}$ is incident on a metal surface. The maximum kinetic energy of the emitted photoelectrons is $1.2\text{ eV}$. Calculate the work function of the metal. [3]
   
   
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4. Explain why the maximum kinetic energy of photoelectrons depends on the frequency of incident radiation but not on the intensity. [3]
   
   
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5. In an X-ray tube, electrons are accelerated through a potential difference of $40\text{ kV}$. Calculate the minimum wavelength ($\lambda_{\min}$) of the X-rays produced. [3]
   
   
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6. Explain why an X-ray spectrum consists of both a continuous distribution of wavelengths and a set of characteristic peaks. [4]
   
   
   
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7. A photon of energy $5.0\text{ eV}$ strikes an electron at rest. Describe the concept of wave-particle duality in the context of the Compton effect. [4]
   
   
   
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Section B: Nuclear Physics (Questions 8–14)

8. Explain what is meant by the binding energy of a nucleus. [2]
   
   
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9. A nucleus of $^{235}\text{U}$ undergoes fission when it absorbs a neutron, splitting into $^{92}\text{Kr}$ and $^{141}\text{Ba}$ and releasing 3 neutrons. Given the mass defect is $0.20\text{ u}$, calculate the total energy released in MeV. [3]
   
   
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10. State the relationship between the binding energy per nucleon and the stability of a nucleus. [2]
    
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11. A radioactive sample has a half-life of $12.0\text{ years}$. If the initial activity is $800\text{ Bq}$, calculate the activity remaining after $36.0\text{ years}$. [3]
    
    
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12. Explain how the age of a moon rock can be determined using the ratio of parent to daughter isotopes in a radioactive decay chain. [4]
    
    
    
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13. Calculate the total kinetic energy of the decay products for a nucleus with a mass defect of $0.015\text{ u}$ during alpha decay. [3]
    
    
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14. Distinguish between nuclear fission and nuclear fusion in terms of the change in binding energy per nucleon. [4]
    
    
    
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Section C: Semiconductors and Lasers (Questions 15–20)

15. Describe the difference between an n-type and a p-type semiconductor in terms of doping. [3]
    
    
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16. Explain the function of a p-n junction diode when it is forward-biased. [3]
    
    
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17. What is the "band gap" in a semiconductor, and how does it differ from the band gap in an insulator? [3]
    
    
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18. State two conditions necessary for the process of stimulated emission to occur in a laser. [3]
    
    
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19. Explain the role of the optical cavity (mirrors) in maintaining the coherence of a laser beam. [4]
    
    
    
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20. A laser emits light of wavelength $632.8\text{ nm}$. Calculate the energy of a single photon emitted by this laser. [3]
    
    
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Answer Key - A-Level Physics H2 Quiz (Modern Physics)

Section A: Quantum Physics

1. $hf = \Phi + E_{k\max}$

   • $h$: Planck's constant
   • $f$: Frequency of incident photon
   • $\Phi$: Work function of the metal
   • $E_{k\max}$: Maximum kinetic energy of the emitted photoelectron. [3]

2. $\Phi = hf_0 \implies f_0 = \Phi / h$ $\Phi = 2.3 \times 1.60 \times 10^{-19} = 3.68 \times 10^{-19}\text{ J}$ $f_0 = (3.68 \times 10^{-19}) / (6.63 \times 10^{-34}) = 5.55 \times 10^{14}\text{ Hz}$. [3]

3. $E_{photon} = hc / \lambda = (6.63 \times 10^{-34} \times 3 \times 10^8) / (300 \times 10^{-9}) = 6.63 \times 10^{-19}\text{ J}$ $E_{photon} \text{ in eV} = 6.63 \times 10^{-19} / 1.60 \times 10^{-19} = 4.14\text{ eV}$ $\Phi = E_{photon} - E_{k\max} = 4.14 - 1.2 = 2.94\text{ eV}$. [3]

4. One-to-one interaction between a photon and an electron. Frequency determines the energy of the individual photon; if $hf > \Phi$, the electron is ejected with $E_k = hf - \Phi$. Intensity only increases the number of photons (and thus the number of electrons), not the energy of each. [3]

5. $E = eV = 40,000 \times 1.60 \times 10^{-19} = 6.4 \times 10^{-15}\text{ J}$ $\lambda_{\min} = hc / E = (6.63 \times 10^{-34} \times 3 \times 10^8) / (6.4 \times 10^{-15}) = 3.11 \times 10^{-11}\text{ m}$. [3]

6. Continuous: Bremsstrahlung (braking radiation) where electrons decelerate by different amounts, emitting photons of varying energies. Characteristic: Electrons knock out inner-shell electrons; outer-shell electrons drop down, emitting photons of specific, discrete energies. [4]

7. Particle nature: Photon behaves as a particle with momentum $p = h/\lambda$, colliding with the electron. Wave nature: The resulting change in wavelength (shift) is described by the wave properties of the radiation. [4]

Section B: Nuclear Physics

8. The energy required to completely separate a nucleus into its constituent protons and neutrons. [2]

9. $E = \Delta m \times 931.5\text{ MeV/u}$ $E = 0.20 \times 931.5 = 186.3\text{ MeV}$. [3]

10. Higher binding energy per nucleon indicates a more stable nucleus. [2]

11. $n = 36 / 12 = 3$ half-lives. $A = A_0 \times (1/2)^3 = 800 / 8 = 100\text{ Bq}$. [3]

12. Radioactive decay follows $N = N_0 e^{-\lambda t}$. By measuring the current amount of parent isotope and the accumulated daughter isotope, the time elapsed since the rock solidified (when daughter was zero) can be calculated using the known decay constant $\lambda$. [4]

13. $E = 0.015 \times 931.5 = 13.97\text{ MeV}$ (or $0.015 \times 1.66 \times 10^{-27} \times (3 \times 10^8)^2 = 2.24 \times 10^{-13}\text{ J}$). [3]

14. Fission: Heavy nucleus splits into lighter nuclei; binding energy per nucleon increases. Fusion: Light nuclei combine into a heavier nucleus; binding energy per nucleon increases. Both processes release energy because the products are more stable (higher BE per nucleon). [4]

Section C: Semiconductors and Lasers

15. n-type: Doped with pentavalent impurities (e.g., Phosphorus), providing extra free electrons. p-type: Doped with trivalent impurities (e.g., Boron), creating "holes" (absence of electrons). [3]

16. The depletion region narrows. Electrons from the n-side and holes from the p-side are pushed toward the junction, allowing current to flow across the junction. [3]

17. Band gap: The energy difference between the valence band and the conduction band. Semiconductor: Small band gap, electrons can be thermally excited. Insulator: Large band gap, electrons cannot easily jump to the conduction band. [3]

18. (1) Population Inversion: More atoms in the excited state than the ground state. (2) Trigger photon: A photon of energy exactly equal to the transition energy to stimulate the drop. [3]

19. Mirrors reflect photons back and forth through the gain medium. This increases the probability of further stimulated emission, ensuring the photons are in phase (coherent) and traveling in the same direction. [4]

20. $E = hc / \lambda = (6.63 \times 10^{-34} \times 3 \times 10^8) / (632.8 \times 10^{-9}) = 3.14 \times 10^{-19}\text{ J}$. [3]