A Level H1 Physics Modern Physics Quiz

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A-Level Physics H1 Quiz - Modern Physics

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

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

Instructions:

• Answer all 20 questions.
• Show your working clearly for calculation questions.
• Use the provided data sheet if needed: $c = 3.00 \times 10^8\ \text{m s}^{-1}$, $u = 1.66 \times 10^{-27}\ \text{kg}$, $e = 1.60 \times 10^{-19}\ \text{C}$.
• Section A: Short Answer (1–5)
• Section B: Calculation (6–12)
• Section C: Structured & Data-Based (13–20)

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Section A: Short Answer (1–5)

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

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2. Define mass defect of a nucleus. [1]

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3. Write the nuclear equation for the alpha decay of $^{226}_{88}\text{Ra}$. [1]

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4. State the principle of radioactive decay and how half-life is defined. [2]

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5. What is meant by binding energy of a nucleus? [1]

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Section B: Calculation (6–12)

6. A sample contains $4.0 \times 10^{20}$ atoms of a radioactive isotope with decay constant $\lambda = 2.5 \times 10^{-6}\ \text{s}^{-1}$. Calculate the initial activity of the sample. [2]

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7. The half-life of a substance is 12 hours. A sample initially has $N_0 = 8.0 \times 10^{18}$ atoms. Calculate the number of atoms remaining after 36 hours. [2]

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8. The mass of a proton is $1.00728\ u$ and a neutron is $1.00867\ u$. The measured mass of a $^2_1\text{H}$ (deuterium) nucleus is $2.01355\ u$. Calculate the mass defect in kg. [3]

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9. Using $E = \Delta m\, c^2$, calculate the binding energy of deuterium in J, given $\Delta m = 0.00240\ u$. [2]

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10. A radioactive source has activity $A = 1.2 \times 10^8\ \text{Bq}$ and decay constant $\lambda = 4.0 \times 10^{-9}\ \text{s}^{-1}$. Determine the number of undecayed nuclei present. [2]

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11. The binding energy per nucleon of $^{56}_{26}\text{Fe}$ is $8.79\ \text{MeV}$. Calculate the total binding energy in MeV and in J. ($1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$) [3]

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12. Carbon-14 has half-life 5730 years. A sample shows activity 25% of its original. Calculate the age of the sample in years. [2]

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Section C: Structured & Data-Based (13–20)

13. (a) State two differences between alpha and beta decay. [2]
(b) Explain why gamma emission does not change the mass number. [1]

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14. A nucleus $^{A}_{Z}X$ undergoes beta-minus decay. Write the general form of the decay equation and state what happens to $Z$ and $A$. [2]

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15. The table shows count rates from a radioactive source over time.

Time (min)	Count rate (s⁻¹)
0	800
2	400
4	200
6	100

(a) Determine the half-life from the table. [1]
(b) Calculate the decay constant $\lambda$ in min⁻¹. [2]

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16.

Image pending generation: graph for Q16.

Using the graph, (a) find the gradient; (b) hence determine the decay constant $\lambda$; (c) state the initial number $N_0$. [3]

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17. A reactor converts mass to energy at rate $P = 500\ \text{MW}$. Calculate the mass converted per day using $E = mc^2$. [3]

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18. (a) Define activity of a radioactive sample. [1]
(b) The activity drops from $A_0$ to $A_0/4$ in 20 days. Find the half-life. [2]

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19. Compare fission and fusion in terms of binding energy per nucleon and energy release. [3]

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20. A sample of $^{131}_{53}\text{I}$ (half-life 8.0 days) has initial mass 0.20 mg. (a) Calculate initial number of nuclei. (b) Activity after 16 days. [4]

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A-Level Physics H1 Quiz - Modern Physics (Answers)

Total Marks: 40

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Section A

1. [1] A nuclide is a species of atom characterised by its number of protons and neutrons (nucleon number A and proton number Z).
Teaching note: Use "specific nucleus with given Z and A". Common mistake: calling it just "atom".

2. [1] Mass defect is the difference between the sum of masses of free constituent nucleons and the actual mass of the bound nucleus.
$\Delta m = Z m_p + (A-Z)m_n - m_{\text{nucleus}}$

3. [1] $^{226}_{88}\text{Ra} \rightarrow\ ^{222}_{86}\text{Rn} +\ ^{4}_{2}\alpha$
Check: A: 226→222+4, Z: 88→86+2.

4. [2] Radioactive decay: random and spontaneous; nucleus decays independently. Half-life: time for half the undecayed nuclei (or activity) to decay. [1+1]

5. [1] Binding energy = minimum energy required to separate nucleus into its constituent protons and neutrons.

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Section B

6. [2] $A = \lambda N = (2.5\times10^{-6})(4.0\times10^{20}) = 1.0\times10^{15}\ \text{Bq}$. [M1 for formula, A1 answer]

7. [2] 36 h = 3 half-lives. $N = N_0 (1/2)^3 = 8.0\times10^{18} / 8 = 1.0\times10^{18}$. [M1: 3 half-lives, A1]

8. [3] Sum = $1.00728 + 1.00867 = 2.01595\ u$. Defect = $2.01595 - 2.01355 = 0.00240\ u$. In kg: $0.00240 \times 1.66\times10^{-27} = 3.98\times10^{-30}\ \text{kg}$. [M1 sum, M1 diff, A1 kg]

9. [2] $\Delta m = 0.00240 \times 1.66\times10^{-27} = 3.98\times10^{-30}\ \text{kg}$. $E = mc^2 = (3.98\times10^{-30})(3.00\times10^8)^2 = 3.59\times10^{-13}\ \text{J}$. [M1 mass, A1 energy]

10. [2] $N = A/\lambda = (1.2\times10^8)/(4.0\times10^{-9}) = 3.0\times10^{16}$. [M1 formula, A1]

11. [3] Total BE = $56 \times 8.79 = 492.2\ \text{MeV}$. In J: $492.2\times10^6 \times 1.60\times10^{-19} = 7.88\times10^{-11}\ \text{J}$. [M1 MeV, M1 J, A1]

12. [2] 25% = $(1/2)^2$ → 2 half-lives. Age = $2 \times 5730 = 11460\ \text{years}$. [M1 factor, A1]

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Section C

13. [3] (a) Alpha: helium nucleus $^4_2\text{He}$, high ionisation, low penetration; Beta: electron, lower ionisation, higher penetration. [1+1] (b) Gamma is photon, no mass/charge change. [1]

14. [2] $^A_ZX \rightarrow\ ^A_{Z+1}Y +\ ^0_{-1}e + \bar{\nu}$. Z increases by 1, A unchanged. [1 eq, 1 statement]

15. [3] (a) Half-life = 2 min (800→400). [1] (b) $\lambda = \ln2 / T_{1/2} = 0.693/2 = 0.347\ \text{min}^{-1}$. [M1, A1]

16. [3] (a) Gradient = $(14-20)/(150-0) = -0.040\ \text{s}^{-1}$. [1] (b) $\lambda = -\text{grad} = 0.040\ \text{s}^{-1}$. [1] (c) At t=0, ln N = 20 → $N_0 = e^{20} = 4.85\times10^8$. [1]
Graph must show straight line, negative slope.

17. [3] Energy/day = $500\times10^6 \times 86400 = 4.32\times10^{13}\ \text{J}$. $m = E/c^2 = 4.32\times10^{13} / 9\times10^{16} = 4.8\times10^{-4}\ \text{kg}$. [M1 E, M1 m, A1]

18. [3] (a) Activity = number of decays per unit time, $A = \lambda N$. [1] (b) $A_0/4$ = 2 half-lives → $T_{1/2}=10$ days. [M1, A1]

19. [3] Fission: heavy nucleus splits, moves toward higher BE/nucleon (mid-mass), releases energy. Fusion: light nuclei join, also to higher BE/nucleon, releases energy. [1+1+1]

20. [4] (a) $N_0 = m/u = 0.20\times10^{-6} / 1.66\times10^{-27} = 1.20\times10^{20}$ (using $u$ as nucleon mass approx; or molar mass method). (b) 16 d = 2 half-lives, $A = A_0/4$, $A_0 = \lambda N_0$, $\lambda = \ln2/ (8\times86400) = 1.00\times10^{-6}\ \text{s}^{-1}$, $A = (1.00\times10^{-6}\times1.20\times10^{20})/4 = 3.0\times10^{13}\ \text{Bq}$. [M1 N0, M1 λ, M1 A0, A1]