A Level H2 Physics Modern Physics Quiz

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A-Level Physics H2 Quiz - Modern Physics

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

Duration: 60 minutes
Total Marks: 40
Topic: Modern Physics (Syllabus 9478)

Instructions:

• Answer all 20 questions.
• Section A: Short structured questions (1–10). Section B: Data and calculation (11–15). Section C: Extended response (16–20).
• Show all working clearly. Use SI units.
• Useful constants: $h = 6.63 \times 10^{-34}\ \text{J s}$, $c = 3.00 \times 10^{8}\ \text{m s}^{-1}$, $e = 1.60 \times 10^{-19}\ \text{C}$, $m_e = 9.11 \times 10^{-31}\ \text{kg}$, $u = 1.66 \times 10^{-27}\ \text{kg}$.

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Section A: Short Structured Questions (1–10)

1. [2 marks] State the photoelectric effect and name one condition required for it to occur.

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2. [1 mark] Write the equation relating photon energy $E$ to frequency $f$.

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3. [2 marks] A metal has a work function $\phi = 2.0\ \text{eV}$. Calculate the threshold frequency $f_0$ in Hz. ($1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$, $h = 6.63 \times 10^{-34}\ \text{J s}$)

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4. [1 mark] State de Broglie's relation between wavelength $\lambda$ and momentum $p$.

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5. [2 marks] An electron is accelerated through a potential difference of $100\ \text{V}$. Calculate its de Broglie wavelength. ($m_e = 9.11 \times 10^{-31}\ \text{kg}$, $e = 1.60 \times 10^{-19}\ \text{C}$, $h = 6.63 \times 10^{-34}\ \text{J s}$)

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6. [1 mark] Complete the nuclear decay equation: ${}_{92}^{238}\text{U} \rightarrow {}_{90}^{234}\text{Th} + \text{?}$

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7. [2 marks] A radioactive sample has half-life $T_{1/2} = 5.0\ \text{h}$. If initial nuclei $N_0 = 8000$, calculate the number remaining after $15\ \text{h}$.

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

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9. [2 marks] Calculate the mass defect of ${}_{2}^{4}\text{He}$ given: mass of ${}_{2}^{4}\text{He} = 4.00260\ \text{u}$, $m_p = 1.00728\ \text{u}$, $m_n = 1.00867\ \text{u}$. ($1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg}$)

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10. [1 mark] State the energy equivalent of $1\ \text{u}$ in MeV. ($c = 3.00 \times 10^{8}\ \text{m s}^{-1}$)

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Section B: Data and Calculation (11–15)

11. [3 marks] Light of wavelength $400\ \text{nm}$ is incident on a metal of work function $1.5\ \text{eV}$. Calculate the maximum kinetic energy of emitted photoelectrons in eV.

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12. [3 marks] A radioactive isotope decays from $N_0 = 1200$ to $N = 150$ in $24\ \text{h}$. Determine the decay constant $\lambda$ in $\text{h}^{-1}$ and the half-life.

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13. [3 marks] The mass of a ${}_{26}^{56}\text{Fe}$ nucleus is $55.92066\ \text{u}$. Constituent nucleons total $56.44932\ \text{u}$. Calculate binding energy per nucleon in MeV. ($1\ \text{u} = 931.5\ \text{MeV}/c^2$)

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14. [3 marks] A proton moves with kinetic energy $2.0\ \text{MeV}$. Calculate its de Broglie wavelength. ($m_p = 1.67 \times 10^{-27}\ \text{kg}$, $1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$, $h = 6.63 \times 10^{-34}\ \text{J s}$)

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15. [3 marks] In a fission reaction, $0.20\ \text{u}$ of mass is converted to energy. Calculate the energy released in MeV and in joules.

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Section C: Extended Response (16–20)

16. [4 marks] Describe the evidence for the wave nature of particles and explain how the de Broglie hypothesis accounts for it.

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17. [4 marks] Explain the concept of mass defect and binding energy. A nucleus has binding energy $B$. Write the relation between mass of separated nucleons $M_{\text{sep}}$, nuclear mass $M$, and $B$.

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18. [4 marks] A photoelectric cell uses light of frequency $f$. Sketch the graph of maximum kinetic energy $K_{\max}$ versus $f$ and state its gradient and intercept.

Image pending generation: graph for Q18.

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19. [4 marks] State the law of radioactive decay and derive the relation $N = N_0 e^{-\lambda t}$ from it.

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20. [4 marks] Compare alpha, beta, and gamma emissions in terms of nature, penetration, and ionizing power.

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A-Level Physics H2 Quiz - Modern Physics (Answers)

Total Marks: 40
Topic: Modern Physics

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Section A Answers (1–10)

1. [2 marks]
Photoelectric effect: emission of electrons from a metal surface when electromagnetic radiation of sufficient frequency shines on it.
Condition: frequency of incident light must exceed threshold frequency $f_0$ (or photon energy $hf > \phi$).
Marking: 1 mark for effect, 1 mark for condition.

2. [1 mark]
$E = hf$
Marking: correct equation with symbols.

3. [2 marks]
$\phi = 2.0 \times 1.60 \times 10^{-19} = 3.20 \times 10^{-19}\ \text{J}$
$f_0 = \phi / h = 3.20 \times 10^{-19} / 6.63 \times 10^{-34} = 4.83 \times 10^{14}\ \text{Hz}$
Marking: 1 mark conversion, 1 mark calculation.

4. [1 mark]
$\lambda = h / p$
Marking: correct formula.

5. [2 marks]
$K = eV = 1.60 \times 10^{-19} \times 100 = 1.60 \times 10^{-17}\ \text{J}$
$p = \sqrt{2mK} = \sqrt{2 \times 9.11 \times 10^{-31} \times 1.60 \times 10^{-17}} = 1.71 \times 10^{-23}\ \text{kg m s}^{-1}$
$\lambda = h/p = 6.63 \times 10^{-34} / 1.71 \times 10^{-23} = 3.88 \times 10^{-11}\ \text{m}$
Marking: 1 mark momentum, 1 mark wavelength.

6. [1 mark]
${}_{2}^{4}\text{He}$ (alpha particle)
Marking: correct particle.

7. [2 marks]
$n = 15/5 = 3$ half-lives
$N = N_0 / 2^3 = 8000 / 8 = 1000$
Marking: 1 mark for n, 1 mark for N.

8. [1 mark]
Energy required to separate nucleus into its constituent protons and neutrons.
Marking: clear definition.

9. [2 marks]
Mass of parts = $2(1.00728) + 2(1.00867) = 4.03190\ \text{u}$
Defect = $4.03190 - 4.00260 = 0.02930\ \text{u}$
$= 0.02930 \times 1.66 \times 10^{-27} = 4.86 \times 10^{-29}\ \text{kg}$
Marking: 1 mark mass diff, 1 mark kg conversion.

10. [1 mark]
$931.5\ \text{MeV}$ (from $E = mc^2$ with $1\ \text{u}$)
Marking: correct value.

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Section B Answers (11–15)

11. [3 marks]
$E_{\text{photon}} = hc/\lambda = (6.63\times10^{-34} \times 3.00\times10^8)/(400\times10^{-9}) = 4.97\times10^{-19}\ \text{J} = 3.11\ \text{eV}$
$K_{\max} = 3.11 - 1.5 = 1.61\ \text{eV}$
Marking: 1 photon energy, 1 conversion, 1 KE.

12. [3 marks]
$N = N_0 e^{-\lambda t} \Rightarrow 150 = 1200 e^{-24\lambda} \Rightarrow e^{-24\lambda} = 0.125$
$-24\lambda = \ln 0.125 = -2.079 \Rightarrow \lambda = 0.0866\ \text{h}^{-1}$
$T_{1/2} = \ln 2 / \lambda = 0.693 / 0.0866 = 8.0\ \text{h}$
Marking: 1 eqn, 1 lambda, 1 half-life.

13. [3 marks]
$\Delta m = 56.44932 - 55.92066 = 0.52866\ \text{u}$
$B = 0.52866 \times 931.5 = 492.4\ \text{MeV}$
Per nucleon = $492.4 / 56 = 8.79\ \text{MeV}$
Marking: 1 defect, 1 total, 1 per nucleon.

14. [3 marks]
$K = 2.0\times10^6 \times 1.60\times10^{-19} = 3.20\times10^{-13}\ \text{J}$
$p = \sqrt{2mK} = \sqrt{2 \times 1.67\times10^{-27} \times 3.20\times10^{-13}} = 3.27\times10^{-20}$
$\lambda = h/p = 6.63\times10^{-34} / 3.27\times10^{-20} = 2.03\times10^{-14}\ \text{m}$
Marking: 1 K, 1 p, 1 lambda.

15. [3 marks]
$E = 0.20 \times 931.5 = 186.3\ \text{MeV}$
In J: $0.20 \times 1.66\times10^{-27} \times (3.00\times10^8)^2 = 2.98\times10^{-11}\ \text{J}$
Marking: 1 MeV, 1 J formula, 1 value.

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Section C Answers (16–20)

16. [4 marks]

• Evidence: electron diffraction (Davisson-Germer) shows interference pattern (2 marks).
• de Broglie: $\lambda = h/p$ gives particles wave-like property; explains diffraction (2 marks).
  Teaching: connect wavelength to momentum.

17. [4 marks]
Mass defect: difference between mass of separated nucleons and nucleus (2). Binding energy: energy equivalent via $E = \Delta m c^2$ (1). Relation: $B = (M_{\text{sep}} - M)c^2$ (1).

18. [4 marks]
Graph: straight line, gradient $h$, intercept $- \phi$ on K axis, x-intercept $f_0$ (2). Explanation: $K_{\max} = hf - \phi$ (2).
Image must show labelled axes and intercepts.

19. [4 marks]
Law: rate of decay proportional to N: $dN/dt = -\lambda N$ (2). Integrate: $\int dN/N = -\lambda \int dt \Rightarrow \ln(N/N_0) = -\lambda t \Rightarrow N = N_0 e^{-\lambda t}$ (2).

20. [4 marks]
Alpha: He nucleus, low penetration, high ionization (1). Beta: electron, medium penetration, medium ionization (1). Gamma: photon, high penetration, low ionization (2).