A Level H2 Physics Modern Physics Quiz

<!-- TuitionGoWhere generation metadata: stage=5-1; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 4-0 LLM templates, syllabus context, and Stage 2 evidence where available. -->

A-Level Physics H2 Quiz - Modern Physics

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 50 minutes
Total Marks: 40

Instructions:

• Answer all 20 questions.
• Show your working clearly where calculations are required.
• Use the data booklet values where needed: $h = 6.63 \times 10^{-34}\text{ J s}$, $c = 3.00 \times 10^8\text{ m s}^{-1}$, $e = 1.60 \times 10^{-19}\text{ C}$, $m_e = 9.11 \times 10^{-31}\text{ kg}$, $u = 1.66 \times 10^{-27}\text{ kg}$.
• This quiz is syllabus-first practice content generated from LLM-inferred templates; it is not derived from official past-year papers.

---

Section A: Photons and Matter Waves (Questions 1–5)

1. A metal surface has a work function of $2.10\text{ eV}$. Light of frequency $9.00 \times 10^{14}\text{ Hz}$ is incident on it. Calculate the maximum kinetic energy, in eV, of the emitted photoelectrons. [3]

---

2. State the de Broglie wavelength equation and define each symbol. [2]

---

3. An electron is accelerated through a potential difference of $150\text{ V}$. Calculate its de Broglie wavelength in nm. [3]

---

4. Explain why the photoelectric effect cannot be explained by a purely wave model of light. [2]

---

5. A photon has energy $3.98 \times 10^{-19}\text{ J}$. Determine its wavelength in nm. [2]

---

---

Section B: Nuclear Physics and Radioactivity (Questions 6–10)

6. Write the balanced nuclear equation for the alpha decay of $^{238}_{92}\text{U}$. [2]

---

7. The half-life of a radioactive isotope is $12.0\text{ h}$. A sample initially contains $4.80 \times 10^{20}$ nuclei. Calculate the number of nuclei remaining after $36.0\text{ h}$. [2]

---

8. Define binding energy of a nucleus. [1]

---

9. Calculate the mass defect of $^{4}_{2}\text{He}$ given: mass of $^{4}_{2}\text{He} = 4.00260\text{ u}$, mass of proton $= 1.00728\text{ u}$, mass of neutron $= 1.00867\text{ u}$. [3]

---

10. A radioactive source emits $\beta^-$ particles. State the change in the nucleus during $\beta^-$ decay. [1]

---

---

Section C: Quantum and Wave-Particle Duality (Questions 11–15)

11. In an electron diffraction experiment, electrons of momentum $p$ produce a first-order maximum at angle $\theta$ using a crystal spacing $d$. State the condition for the first maximum. [1]

---

12. A laser of wavelength $632\text{ nm}$ is directed at a double slit of separation $0.200\text{ mm}$. The screen is $1.50\text{ m}$ away. Calculate the fringe separation. [3]

---

13. The graph below shows photocurrent against anode voltage for two light intensities.

Image pending generation: graph for Q13.

State what the graph shows about the effect of light intensity on stopping potential and saturation current. [2]

---

14. Calculate the energy, in MeV, equivalent to a mass defect of $0.00850\text{ u}$. [2]

---

15. Explain how the existence of a threshold frequency in the photoelectric effect supports a particle model of light. [2]

---

---

Section D: Mixed Modern Physics (Questions 16–20)

16. A nucleus $^{14}_{7}\text{N}$ captures a neutron and emits a proton. Write the resulting nuclide equation. [2]

---

17. The activity of a sample falls from $800\text{ Bq}$ to $100\text{ Bq}$ in $30\text{ s}$. Calculate the decay constant $\lambda$ in s$^{-1}$. [3]

---

18. An X-ray photon has wavelength $0.100\text{ nm}$. Calculate its momentum. [2]

---

19.

Image pending generation: diagram for Q19.

Calculate the wavelength of the photon emitted in the transition E3 → E1. [3]

---

20. State one piece of experimental evidence for the wave nature of matter. [1]

---

<!-- TuitionGoWhere generation metadata: stage=5-1; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 4-0 LLM templates, syllabus context, and Stage 2 evidence where available. -->

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

Total Marks: 40
Syllabus-first practice content from LLM-inferred templates; not official past-year derived.

---

Section A: Photons and Matter Waves

1. [3 marks]
Work function $\phi = 2.10\text{ eV} = 2.10 \times 1.60\times10^{-19} = 3.36\times10^{-19}\text{ J}$.
Photon energy $E = hf = (6.63\times10^{-34})(9.00\times10^{14}) = 5.97\times10^{-19}\text{ J}$.
$K_{\max} = E - \phi = 5.97\times10^{-19} - 3.36\times10^{-19} = 2.61\times10^{-19}\text{ J}$.
In eV: $2.61\times10^{-19} / 1.60\times10^{-19} = 1.63\text{ eV}$.
Answer: $1.63\text{ eV}$ (accept 1.6 eV).
Teaching note: Use $E = hf - \phi$. Convert eV to J if needed; here final in eV so divide by e.

2. [2 marks]
$\lambda = \frac{h}{p}$ where $\lambda$ = de Broglie wavelength, $h$ = Planck constant, $p$ = momentum of particle.
Answer: equation + definitions (1+1).
Common mistake: writing $p = mv$ only without stating $\lambda$.

3. [3 marks]
Kinetic energy gained $E_k = eV = 150\text{ eV} = 150 \times 1.60\times10^{-19} = 2.40\times10^{-17}\text{ J}$.
$p = \sqrt{2m_e E_k} = \sqrt{2(9.11\times10^{-31})(2.40\times10^{-17})} = 6.61\times10^{-24}\text{ kg m s}^{-1}$.
$\lambda = h/p = 6.63\times10^{-34} / 6.61\times10^{-24} = 1.00\times10^{-10}\text{ m} = 0.100\text{ nm}$.
Answer: $0.100\text{ nm}$.
Marking: 1 for KE, 1 for p, 1 for λ.

4. [2 marks]
A wave model predicts energy depends on intensity, so higher intensity should eject electrons at any frequency; but experiment shows no emission below threshold frequency regardless of intensity, and emission is instantaneous. This implies energy is quantised in photons.
Answer: any two correct points.

5. [2 marks]
$E = hc/\lambda \Rightarrow \lambda = hc/E = (6.63\times10^{-34})(3.00\times10^8) / (3.98\times10^{-19}) = 5.00\times10^{-7}\text{ m} = 500\text{ nm}$.
Answer: $500\text{ nm}$.

---

Section B: Nuclear Physics and Radioactivity

6. [2 marks]
$^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\alpha$.
Marking: 1 for daughter nucleus, 1 for alpha particle with balances.

7. [2 marks]
$36.0 / 12.0 = 3$ half-lives. $N = N_0 (1/2)^3 = 4.80\times10^{20} \times 1/8 = 6.00\times10^{19}$.
Answer: $6.00\times10^{19}$.

8. [1 mark]
Binding energy is the minimum energy required to separate a nucleus into its constituent protons and neutrons.

9. [3 marks]
Mass of 2p + 2n = $2(1.00728) + 2(1.00867) = 4.03190\text{ u}$.
Mass defect $\Delta m = 4.03190 - 4.00260 = 0.02930\text{ u}$.
Answer: $0.0293\text{ u}$.
Marking: 1 for constituent mass, 1 for subtraction, 1 for value.

10. [1 mark]
A neutron changes into a proton with emission of an electron ($\beta^-$) and antineutrino; atomic number increases by 1.

---

Section C: Quantum and Wave-Particle Duality

11. [1 mark]
$d\sin\theta = \lambda$ (or $d\sin\theta = h/p$ for first order, $n=1$).

12. [3 marks]
$\Delta x = \lambda D / a = (632\times10^{-9})(1.50) / (0.200\times10^{-3}) = 4.74\times10^{-3}\text{ m} = 4.74\text{ mm}$.
Answer: $4.74\text{ mm}$.
Marking: 1 formula, 1 substitution, 1 answer.

13. [2 marks]
Stopping potential is the same for both intensities (photon energy unchanged); saturation current is larger for higher intensity (more photons per second).
From image: both curves hit zero at -1.5 V; I1 saturates higher.

14. [2 marks]
$1\text{ u} = 931.5\text{ MeV}$. $E = 0.00850 \times 931.5 = 7.92\text{ MeV}$.
Answer: $7.92\text{ MeV}$.

15. [2 marks]
Below threshold frequency no electrons are emitted no matter how intense the light; this shows light energy is delivered in discrete packets (photons) with $E=hf$, so only $f$ matters, not wave amplitude.

---

Section D: Mixed Modern Physics

16. [2 marks]
$^{14}_{7}\text{N} + ^{1}_{0}\text{n} \rightarrow ^{14}_{6}\text{C} + ^{1}_{1}\text{p}$.
Resulting nuclide is carbon-14.

17. [3 marks]
$A = A_0 e^{-\lambda t} \Rightarrow 100 = 800 e^{-30\lambda} \Rightarrow 1/8 = e^{-30\lambda}$.
$\ln(1/8) = -30\lambda \Rightarrow -2.079 = -30\lambda \Rightarrow \lambda = 0.0693\text{ s}^{-1}$.
Answer: $0.0693\text{ s}^{-1}$.

18. [2 marks]
$p = h/\lambda = 6.63\times10^{-34} / (0.100\times10^{-9}) = 6.63\times10^{-24}\text{ kg m s}^{-1}$.
Answer: $6.63\times10^{-24}\text{ kg m s}^{-1}$.

19. [3 marks]
$\Delta E = E3 - E1 = -2.0 - (-10.0) = 8.0\text{ eV} = 8.0 \times 1.60\times10^{-19} = 1.28\times10^{-18}\text{ J}$.
$\lambda = hc/\Delta E = (6.63\times10^{-34})(3.00\times10^8) / (1.28\times10^{-18}) = 1.55\times10^{-7}\text{ m} = 155\text{ nm}$.
Answer: $155\text{ nm}$.

20. [1 mark]
Electron diffraction (e.g. by crystal) or Davisson-Germer experiment.