A Level H1 Physics Modern Physics Quiz

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A-Level Physics H1 Quiz - Modern Physics

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

Duration: 50 minutes
Total Marks: 40
Topic: Modern Physics (Nuclear Physics – Syllabus 8867 Topic 11)

Instructions:

• Answer all 20 questions.
• Show your working clearly for calculation questions.
• Use the provided data sheet values where needed:
  Speed of light $c = 3.00 \times 10^8\ \text{m s}^{-1}$
  $1\ \text{u} = 931.5\ \text{MeV}/c^2$
  $\ln 2 = 0.693$
• Section A: Short recall and concepts (1–7)
  Section B: Calculations (8–14)
  Section C: Data interpretation and structured response (15–20)

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Section A: Concepts and Recall (14 marks)

1. State what is meant by the term nuclide. [1]

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2. Define mass defect of a nucleus. [2]

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3. The following nuclear equation represents alpha decay:
$^{238}_{92}\text{U} \rightarrow ^{A}_{Z}\text{X} + ^{4}_{2}\alpha$
State the values of $A$ and $Z$. [2]

$A =$ _________
$Z =$ _________

4. Explain why beta-minus ($\beta^-$) decay results in the atomic number increasing by 1 but the mass number staying the same. [2]

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5. A radioactive sample has a half-life of 4.0 hours. State what is meant by half-life. [1]

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6. Write the nuclear equation for the beta-plus ($\beta^+$) decay of $^{22}_{11}\text{Na}$. [2]

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7. State one safety precaution when handling radioactive sources in a school laboratory. [1]

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Section B: Calculations (14 marks)

8. A nucleus $^{12}_{6}\text{C}$ has a mass of $12.0000\ \text{u}$. The total mass of its 6 protons and 6 neutrons is $12.0984\ \text{u}$. Calculate the mass defect in atomic mass units (u). [2]

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9. Using your answer from Q8 and $1\ \text{u} = 931.5\ \text{MeV}/c^2$, calculate the binding energy of $^{12}_{6}\text{C}$ in MeV. [2]

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10. A radioactive isotope has a decay constant $\lambda = 0.050\ \text{h}^{-1}$. Calculate its half-life in hours. [2]

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11. A sample initially contains $N_0 = 800$ nuclei of a radioactive isotope. After 12 days, 100 nuclei remain. Determine the half-life of the isotope in days. [2]

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12. In a fission reaction, the mass lost is $0.200\ \text{u}$. Given $1\ \text{u} = 1.66 \times 10^{-27}\ \text{kg}$ and $c = 3.00 \times 10^8\ \text{m s}^{-1}$, calculate the energy released in joules. [3]

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13. $^{226}_{88}\text{Ra}$ decays by alpha emission to $^{222}_{86}\text{Rn}$. Write the balanced nuclear equation and calculate the kinetic energy released if the mass difference is $0.0053\ \text{u}$, in MeV. [3]

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14. A radioactive source has activity $A = 2.4 \times 10^6\ \text{Bq}$ and decay constant $\lambda = 1.2 \times 10^{-6}\ \text{s}^{-1}$. Calculate the number of undecayed nuclei present. [2]

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Section C: Data Interpretation and Structured Response (12 marks)

15. The graph shows the decay of a radioactive sample.

Image pending generation: graph for Q15.

Using the graph, determine the decay constant $\lambda$ from the gradient. [2]

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16. From the decay constant in Q15, calculate the half-life of the sample in seconds. [1]

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17. Explain why the binding energy per nucleon versus mass number curve peaks near iron ($^{56}\text{Fe}$) and state the significance for nuclear fusion and fission. [3]

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18. A detector measures background count rate of $20\ \text{s}^{-1}$. With a source present the count rate is $80\ \text{s}^{-1}$. Calculate the corrected count rate due to the source. [1]

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19. Suggest why radioactive dating using carbon-14 is limited to samples less than about 50 000 years old. [2]

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20. Describe how a Geiger-Müller tube detects ionizing radiation, and state one limitation of this detector. [3]

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A-Level Physics H1 Quiz - Modern Physics (Answer Key)

Topic: Modern Physics (Syllabus 8867 Topic 11)
Total Marks: 40
Note: Content generated from syllabus-first LLM templates; not claimed as past-year derived.

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Section A: Concepts and Recall

1. [1 mark]
A nuclide is a species of atom characterised by the number of protons and neutrons in its nucleus (i.e. a specific combination of $Z$ and $A$).
Teaching note: "Nuclide" refers to the nucleus type, not the element alone. Isotopes are nuclides with same $Z$ but different $A$.

2. [2 marks]
Mass defect is the difference between the sum of the masses of the separate nucleons (protons and neutrons) and the actual mass of the bound nucleus.
[1] for "difference in mass"
[1] for "free nucleons vs bound nucleus"
Common mistake: Confusing with binding energy (energy equivalent).

3. [2 marks]
Conservation of nucleon number: $238 = A + 4 \Rightarrow A = 234$
Conservation of charge: $92 = Z + 2 \Rightarrow Z = 90$
$A = 234$, $Z = 90$ [1 each]

4. [2 marks]
In $\beta^-$ decay, a neutron transforms into a proton and an electron (and antineutrino): $n \rightarrow p + e^- + \bar{\nu}_e$.
The proton stays in nucleus so $Z$ increases by 1; the electron is emitted, mass number (nucleon count) unchanged.
[1] for neutron→proton explanation, [1] for mass number unchanged.

5. [1 mark]
Half-life is the time taken for half of the radioactive nuclei in a sample to decay (or activity to halve).

6. [2 marks]
$^{22}_{11}\text{Na} \rightarrow ^{22}_{10}\text{Ne} + ^{0}_{+1}e$ (or $\beta^+$)
[1] for daughter Ne with Z=10, A=22; [1] for positron emitted.

7. [1 mark]
Any one: use tongs/remote handling; store in lead container; limit exposure time; wear badge dosimeter.

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Section B: Calculations

8. [2 marks]
Mass defect $\Delta m = 12.0984 - 12.0000 = 0.0984\ \text{u}$
[2] for correct subtraction and unit.

9. [2 marks]
$E_b = 0.0984 \times 931.5 = 91.7\ \text{MeV}$
[1] method, [1] answer to 3 s.f.

10. [2 marks]
$t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{0.050} = 13.9\ \text{h}$
[1] formula, [1] answer.

11. [2 marks]
$100 = 800 \times (1/2)^{12/T}$
$1/8 = (1/2)^{12/T} \Rightarrow 3 = 12/T \Rightarrow T = 4.0\ \text{days}$
[1] use of halving, [1] answer.

12. [3 marks]
$\Delta m = 0.200 \times 1.66 \times 10^{-27} = 3.32 \times 10^{-28}\ \text{kg}$
$E = \Delta m c^2 = 3.32 \times 10^{-28} \times (3.00 \times 10^8)^2 = 2.99 \times 10^{-11}\ \text{J}$
[1] mass in kg, [1] use $E=mc^2$, [1] answer.

13. [3 marks]
Equation: $^{226}_{88}\text{Ra} \rightarrow ^{222}_{86}\text{Rn} + ^{4}_{2}\alpha$ [1]
$E = 0.0053 \times 931.5 = 4.94\ \text{MeV}$ [2]

14. [2 marks]
$A = \lambda N \Rightarrow N = A/\lambda = 2.4\times10^6 / 1.2\times10^{-6} = 2.0\times10^{12}$
[1] formula, [1] answer.

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Section C: Data Interpretation

15. [2 marks]
Gradient $= (2.7 - 6.9)/(150 - 0) = -4.2/150 = -0.028\ \text{s}^{-1}$
$\lambda = -\text{gradient} = 0.028\ \text{s}^{-1}$
[1] gradient, [1] lambda positive.

16. [1 mark]
$t_{1/2} = 0.693 / 0.028 = 24.8\ \text{s}$

17. [3 marks]
Curve peaks near Fe because nuclei are most tightly bound there. [1]
Fusion of light nuclei moves toward peak, releasing energy. [1]
Fission of heavy nuclei also moves toward peak, releasing energy. [1]

18. [1 mark]
Corrected rate $= 80 - 20 = 60\ \text{s}^{-1}$

19. [2 marks]
After ~50k years, C-14 remaining is too small to measure accurately (less than ~0.1% left). [1]
Background and contamination dominate. [1]

20. [3 marks]
GM tube: ionizing radiation enters, ionizes gas, pulse counted. [2]
Limitation: cannot distinguish radiation types or measure energy. [1]