ETEA / KMU MDCAT (KPK) Physics Nuclear Physics — Set 2

1. Question 1

   Q1. A sample of radioactive material has 4.0 x 10^18 atoms. If its decay constant is 0.02 s^-1, how many atoms decay in 2 seconds?

   • A) 1.28 x 10^18
   • B) 3.20 x 10^17
   • C) 6.40 x 10^17
   • D) 1.60 x 10^18

   Answer: 1.28 x 10^18

   Explanation: Using N = N0 * e^(-λt), we find the remaining atoms, then subtract from initial. Most tempting wrong option 'D' assumes linear decay.

2. Question 2

   Q2. The half-life of a radioactive substance is 10 years. What fraction of the substance remains after 30 years?

   • A) 1/8
   • B) 1/4
   • C) 1/2
   • D) 1/16

   Answer: 1/8

   Explanation: After 3 half-lives, the fraction remaining is (1/2)^3 = 1/8. Option 'C' is wrong as it's after 1 half-life.

3. Question 3

   Q3. A nucleus of Uranium-238 undergoes alpha decay. What is the mass number of the resulting nucleus?

   • A) 234
   • B) 236
   • C) 238
   • D) 240

   Answer: 234

   Explanation: Alpha decay reduces mass number by 4. Resulting nucleus has mass number 238 - 4 = 234. Option 'B' incorrectly adds 2 protons.

4. Question 4

   Q4. The binding energy per nucleon for a nucleus is 8.5 MeV. If the nucleus has 100 nucleons, what is its total binding energy?

   • A) 850 MeV
   • B) 85 MeV
   • C) 8.5 MeV
   • D) 0.085 MeV

   Answer: 850 MeV

   Explanation: Total binding energy = binding energy per nucleon * number of nucleons = 8.5 MeV * 100 = 850 MeV. Option 'B' divides instead of multiplying.

5. Question 5

   Q5. In a nuclear reactor, the moderator is used to

   • A) absorb neutrons
   • B) slow down neutrons
   • C) speed up neutrons
   • D) reflect neutrons

   Answer: slow down neutrons

   Explanation: Moderator slows down neutrons to increase probability of fission. Option 'A' is wrong as it's the function of control rods.

6. Question 6

   Q6. The mass defect of a nucleus is 0.1 u. What is its binding energy?

   • A) 93 MeV
   • B) 93.1 MeV
   • C) 9.3 MeV
   • D) 931 MeV

   Answer: 93 MeV

   Explanation: Binding energy = mass defect * 931 MeV/u = 0.1 u * 931 MeV/u = 93.1 MeV. Option 'C' forgets to multiply by 931.

7. Question 7

   Q7. A radioactive sample has an activity of 1000 Bq. If its decay constant is 0.01 s^-1, how many radioactive atoms are present?

   • A) 100000
   • B) 10000
   • C) 1000
   • D) 50000

   Answer: 100000

   Explanation: Activity = λN, so N = Activity / λ = 1000 / 0.01 = 100000. Option 'B' incorrectly divides by 0.1.

8. Question 8

   Q8. The energy released in a nuclear fission reaction is approximately

   • A) 200 MeV
   • B) 20 MeV
   • C) 2 MeV
   • D) 0.2 MeV

   Answer: 200 MeV

   Explanation: Fission releases around 200 MeV of energy per reaction. Option 'B' underestimates this energy.

9. Question 9

   Q9. In a nuclear fusion reaction, two deuterium nuclei combine to form a helium nucleus. What is the resulting nucleus?

   • A) Helium-4
   • B) Helium-3
   • C) Tritium
   • D) Helium-2

   Answer: Helium-4

   Explanation: Deuterium-deuterium fusion produces Helium-3 and a neutron, or Helium-4 and a gamma ray (less common). Most stable result is Helium-4 (after including the other products).

10. Question 10

    Q10. The count rate of a radioactive sample decreases from 1600 counts per minute to 100 counts per minute in 8 hours. What is its half-life?

    • A) 2 hours
    • B) 1 hour
    • C) 4 hours
    • D) 8 hours

    Answer: 2 hours

    Explanation: Using the formula for count rate and half-life, we can determine that the half-life is 2 hours. Option 'C' misinterprets the count rate directly as half-life.

11. Question 11

    Q11. The decay constant of a radioactive substance is 0.05 s^-1. What is its half-life?

    • A) 13.86 s
    • B) 1.386 s
    • C) 0.1386 s
    • D) 138.6 s

    Answer: 13.86 s

    Explanation: Half-life = ln(2) / λ = 0.693 / 0.05 = 13.86 s. Option 'B' uses wrong value for ln(2).

12. Question 12

    Q12. The mass of a nucleus is less than the sum of the masses of its constituent nucleons. This difference is called

    • A) mass defect
    • B) binding energy
    • C) nuclear energy
    • D) ionization energy

    Answer: mass defect

    Explanation: The mass difference is known as mass defect, which is related to binding energy. Option 'B' confuses the effect (binding energy) with the cause (mass defect).

13. Question 13

    Q13. A sample of Radon-222 has a half-life of 3.8 days. How long will it take for the sample to decay to 1/16 of its original amount?

    • A) 15.2 days
    • B) 7.6 days
    • C) 3.8 days
    • D) 30.4 days

    Answer: 15.2 days

    Explanation: To decay to 1/16, it takes 4 half-lives (1/2)^4 = 1/16. 4 * 3.8 days = 15.2 days. Option 'B' calculates for 2 half-lives.

14. Question 14

    Q14. The energy released when a nucleus is formed from its constituent nucleons is called

    • A) binding energy
    • B) ionization energy
    • C) excitation energy
    • D) nuclear energy

    Answer: binding energy

    Explanation: The energy released is known as binding energy, which holds the nucleus together. Option 'D' is too broad and not specific.

15. Question 15

    Q15. A nucleus undergoes beta decay. What happens to its atomic number?

    • A) Increases by 1
    • B) Decreases by 1
    • C) Remains the same
    • D) Increases by 2

    Answer: Increases by 1

    Explanation: In beta decay, a neutron converts to a proton, increasing the atomic number by 1. Option 'B' is wrong as it's the case for positron emission or electron capture.

16. Question 16

    Q16. The radiation that is most penetrating is

    • A) gamma radiation
    • B) alpha particles
    • C) beta particles
    • D) neutrons

    Answer: gamma radiation

    Explanation: Gamma radiation is the most penetrating due to its lack of charge and mass. Option 'B' is wrong as alpha particles are heavily ionizing but not penetrating.

17. Question 17

    Q17. In a nuclear reaction, mass is converted into energy according to the equation

    • A) E = mc^2
    • B) E = mc
    • C) E = m/c
    • D) E = m/c^2

    Answer: E = mc^2

    Explanation: Einstein's equation relates mass (m) and energy (E) with the speed of light (c). Option 'B' forgets to square 'c'.

18. Question 18

    Q18. The activity of a radioactive sample is 5000 Bq. If the decay constant is 0.02 min^-1, how many nuclei are present?

    • A) 250000
    • B) 25000
    • C) 2500
    • D) 250

    Answer: 250000

    Explanation: Activity = λN, so N = Activity / λ. Converting λ to s^-1, we get N = 5000 / (0.02/60) = 250000. Option 'B' uses λ in min^-1 directly.

19. Question 19

    Q19. A proton and a neutron combine to form a deuterium nucleus, releasing 2.2 MeV of energy. What is the mass defect?

    • A) 0.0024 u
    • B) 0.024 u
    • C) 0.002 u
    • D) 0.24 u

    Answer: 0.0024 u

    Explanation: Mass defect = Energy released / 931 MeV/u = 2.2 MeV / 931 MeV/u = 0.0024 u. Option 'B' incorrectly divides by 93 instead of 931.

20. Question 20

    Q20. The process by which a heavy nucleus splits into two or more lighter nuclei is called

    • A) nuclear fission
    • B) nuclear fusion
    • C) radioactive decay
    • D) nuclear reaction

    Answer: nuclear fission

    Explanation: Nuclear fission is the process of a heavy nucleus splitting. Option 'B' is the opposite process, where lighter nuclei combine.