A Level H1 Physics Modern Physics Quiz

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A-Level Physics H1 Quiz - Modern Physics

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

Duration: 60 Minutes
Total Marks: 60

Instructions:

• Answer all questions.
• 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 $1 \text{ u} = 1.66 \times 10^{-27} \text{ kg}$.
• Show all working clearly for calculation questions.

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Section A: Photoelectric Effect & Quantum Physics (Questions 1-10)

1. Define the term work function of a metal. [2]
   
   
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2. A metal surface has a work function of $2.10 \text{ eV}$. Calculate the threshold frequency $f_0$ for this metal. [3]
   
   
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3. Light of wavelength $350 \text{ nm}$ is incident on a metal with a work function of $2.10 \text{ eV}$. Calculate the maximum kinetic energy of the emitted photoelectrons in electron-volts (eV). [3]
   
   
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4. For the light described in Question 3, determine the stopping potential $V_s$. [2]
   
   
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5. Explain why the emission of photoelectrons occurs instantaneously upon illumination, and why this observation contradicts the classical wave model of light. [3]
   
   
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6. A graph of maximum kinetic energy $K_{\text{max}}$ against frequency $f$ is plotted for a specific metal. (a) State the physical significance of the gradient of this graph. [1] (b) State the physical significance of the $x$-intercept. [1]
   
   
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7. If the intensity of the incident light is increased while keeping the frequency constant (above the threshold), describe the effect on: (a) The maximum kinetic energy of the emitted electrons. [1] (b) The photoelectric current. [1]
   
   
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8. A photon has a momentum of $2.0 \times 10^{-27} \text{ kg m s}^{-1}$. Calculate its wavelength. [3]
   
   
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9. Compare the energy of a photon of blue light ($\lambda = 450 \text{ nm}$) with a photon of red light ($\lambda = 700 \text{ nm}$). Which has higher energy, and by what factor? [3]
   
   
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10. Describe the effect on the stopping potential if the metal surface is replaced by one with a higher work function, provided the incident light frequency remains the same. [3]
    
    
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Section B: Nuclear Structure & Radioactivity (Questions 11-20)

11. Define the term isotope. [2]
    
    
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12. A radioactive sample has an initial activity of $1200 \text{ Bq}$. After $24$ hours, the activity has fallen to $150 \text{ Bq}$. Determine the half-life of the isotope. [3]
    
    
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13. An isotope of Carbon-14 decays via $\beta^-$ emission. Write the nuclear equation for this decay. [3]
    
    
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14. Explain the difference between $\alpha$-decay and $\beta^+$-decay in terms of the change in atomic number and mass number. [4]
    
    
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15. A nucleus has a mass defect of $0.045 \text{ u}$. Calculate the total binding energy of the nucleus in Mega-electronvolts (MeV). [4]
    
    
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16. Define binding energy per nucleon and explain why it is a better measure of nuclear stability than total binding energy. [3]
    
    
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17. A sample of a radioactive isotope contains $N_0$ nuclei. After a time $t$ equal to two half-lives, what fraction of the original nuclei remains undecayed? [2]
    
    
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18. Describe the characteristics of $\gamma$-radiation in terms of its nature, ionizing power, and penetrating power. [3]
    
    
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19. A nucleus $X$ with mass number $A$ and atomic number $Z$ undergoes $\alpha$-decay to become nucleus $Y$. Express the mass number and atomic number of $Y$ in terms of $A$ and $Z$. [2]
    
    
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20. Explain why the binding energy per nucleon curve peaks around Iron-56 ($^{56}\text{Fe}$). [3]
    
    
    
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A-Level Physics H1 Quiz - Modern Physics (Answer Key)

Section A: Photoelectric Effect & Quantum Physics

1. Definition: The minimum energy required for an electron to be released from the surface of a metal. [2]

2. Calculation: $\Phi = 2.10 \text{ eV} = 2.10 \times 1.60 \times 10^{-19} \text{ J} = 3.36 \times 10^{-19} \text{ J}$ $f_0 = \Phi / h = (3.36 \times 10^{-19}) / (6.63 \times 10^{-34}) = 5.07 \times 10^{14} \text{ Hz}$ [3]

3. Calculation: $E_{photon} = hc / \lambda = (6.63 \times 10^{-34} \times 3.00 \times 10^8) / (350 \times 10^{-9}) = 5.68 \times 10^{-19} \text{ J}$ $E_{photon} \text{ in eV} = (5.68 \times 10^{-19}) / (1.60 \times 10^{-19}) = 3.55 \text{ eV}$ $K_{\text{max}} = E_{photon} - \Phi = 3.55 - 2.10 = 1.45 \text{ eV}$ [3]

4. Calculation: $eV_s = K_{\text{max}} \rightarrow V_s = 1.45 \text{ V}$ [2]

5. Explanation:

   • Observation: Electrons are emitted immediately regardless of intensity. [1]
   • Wave model contradiction: Wave model predicts energy would accumulate over time before an electron is ejected, leading to a time lag. [2]

6. Graph Analysis: (a) Gradient = Planck's constant $h$. [1] (b) $x$-intercept = Threshold frequency $f_0$. [1]

7. Intensity Effects: (a) No effect (remains constant). [1] (b) Increases (more photons per second $\rightarrow$ more electrons emitted per second). [1]

8. Calculation: $p = h / \lambda \rightarrow \lambda = h / p = (6.63 \times 10^{-34}) / (2.0 \times 10^{-27}) = 3.32 \times 10^{-7} \text{ m}$ (or $332 \text{ nm}$) [3]

9. Comparison: $E \propto 1/\lambda$. Blue light has a shorter wavelength, so it has higher energy. [1] Factor = $\lambda_{\text{red}} / \lambda_{\text{blue}} = 700 / 450 = 1.56$ [2]

10. Stopping Potential: $K_{\text{max}} = hf - \Phi$. If $\Phi$ increases, $K_{\text{max}}$ decreases. [2] Since $V_s = K_{\text{max}}/e$, the stopping potential will decrease. [1]

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Section B: Nuclear Structure & Radioactivity

11. Definition: Atoms of the same element (same atomic number/protons) that have different mass numbers (different number of neutrons). [2]

12. Calculation: $1200 \rightarrow 600 \rightarrow 300 \rightarrow 150$ (3 half-lives) [1] $3 \times t_{1/2} = 24 \text{ hours} \rightarrow t_{1/2} = 8 \text{ hours}$ [2]

13. Equation: $^{14}_{6}\text{C} \rightarrow ^{14}_{7}\text{N} + ^{0}_{-1}\text{e} + \bar{\nu}_e$ (Antineutrino optional but preferred) [3]

14. Comparison:

    • $\alpha$-decay: Mass number decreases by 4, atomic number decreases by 2. [2]
    • $\beta^+$-decay: Mass number remains unchanged, atomic number decreases by 1. [2]

15. Calculation: $\Delta m = 0.045 \times 1.66 \times 10^{-27} = 7.47 \times 10^{-29} \text{ kg}$ [1] $E = \Delta m c^2 = (7.47 \times 10^{-29}) \times (3.00 \times 10^8)^2 = 6.72 \times 10^{-12} \text{ J}$ [2] $E \text{ in MeV} = (6.72 \times 10^{-12}) / (1.60 \times 10^{-13}) = 42.0 \text{ MeV}$ [1]

16. Binding Energy per Nucleon:

    • Definition: Total binding energy divided by the number of nucleons (A). [1]
    • Significance: It represents the average energy required to remove a nucleon; higher value indicates greater stability regardless of the size of the nucleus. [2]

17. Fraction: After 1 half-life: $1/2$. After 2 half-lives: $1/4$ (or $25\%$). [2]

18. $\gamma$-radiation:

    • Nature: High-energy electromagnetic radiation (photons). [1]
    • Ionizing power: Low. [1]
    • Penetrating power: Very high. [1]

19. Nuclear Equation: Mass number of $Y = A - 4$ [1] Atomic number of $Y = Z - 2$ [1]

20. Stability Curve: Iron-56 has one of the highest binding energies per nucleon. [1] This means it is among the most stable nuclei. [1] Nuclei lighter than Fe undergo fusion, and heavier nuclei undergo fission to move toward this peak of stability. [1]