NUMS MDCAT (Military Medical) Physics Nuclear Physics — Set 3

NUMS MDCAT (Military Medical) Physics Nuclear Physics — Set 3

1. Question 1

   Q1. A nucleus undergoes alpha decay, reducing its mass number by 4 and atomic number by 2. How many neutrons remain in the daughter nucleus if the parent had 146 neutrons and 92 protons?

   • A) 144
   • B) 140
   • C) 142
   • D) 146

   Answer: 140

   Explanation: Neutrons = (Parent protons + neutrons) - decay losses. Alpha decay removes 2 protons and 2 neutrons. Option D fails to subtract 2 neutrons.

2. Question 2

   Q2. A sample of ²³⁸U (half-life 4.5 billion years) has 1/8th the original activity. How many half-lives have elapsed?

   • A) 3
   • B) 4
   • C) 2
   • D) 5

   Answer: 3

   Explanation: Activity halves every half-life. 1/8 = (1/2)^3, so 3 half-lives elapsed. Option B incorrectly adds one more half-life.

3. Question 3

   Q3. If a neutron star converts 0.7% of its mass to energy, what is the energy released? (Given: mass = 2.8 × 10³⁰ kg, c = 3 × 10⁸ m/s)

   • A) 1.8 × 10⁵⁰ J
   • B) 2.1 × 10⁵¹ J
   • C) 1.89 × 10⁵⁰ J
   • D) 1.89 × 10⁵² J

   Answer: 1.89 × 10⁵⁰ J

   Explanation: Use E = Δmc² = 0.007 × 2.8 × 10³⁰ × (9 × 10¹⁶). Option A incorrectly omits the 0.7% conversion factor.

4. Question 4

   Q4. The binding energy of ⁴He is 28.3 MeV. What is its binding energy per nucleon?

   • A) 7.08 MeV
   • B) 14.15 MeV
   • C) 28.3 MeV
   • D) 56.6 MeV

   Answer: 7.08 MeV

   Explanation: Binding energy per nucleon = total BE / mass number. 28.3 MeV / 4 = 7.08 MeV. Option B divides by 2 instead of 4.

5. Question 5

   Q5. In a fission reaction, 0.001 kg of mass is converted to energy. How much energy is released? (c = 3 × 10⁸ m/s)

   • A) 9 × 10¹³ J
   • B) 9 × 10¹⁴ J
   • C) 9 × 10¹² J
   • D) 9 × 10¹¹ J

   Answer: 9 × 10¹³ J

   Explanation: E = mc² = 0.001 × (3 × 10⁸)² = 9 × 10¹³ J. Option B misplaces the decimal.

6. Question 6

   Q6. A nuclear reactor produces 2000 MW for 1 hour. How many joules of energy are generated?

   • A) 7.2 × 10⁹ J
   • B) 7.2 × 10¹⁰ J
   • C) 2 × 10⁹ J
   • D) 2 × 10¹¹ J

   Answer: 7.2 × 10⁹ J

   Explanation: Energy = power × time = 2000 × 10⁶ W × 3600 s = 7.2 × 10⁹ J. Option B miscalculates unit conversion.

7. Question 7

   Q7. If a neutron moderator slows neutrons from 2 MeV to 0.025 eV, what is the ratio of their kinetic energies before and after?

   • A) 80000:1
   • B) 1:80000
   • C) 1000:1
   • D) 1:1000

   Answer: 80000:1

   Explanation: Energy ratio = 2 × 10⁶ eV / 0.025 eV = 80,000. Option C ignores the correct unit conversion.

8. Question 8

   Q8. A ³²P sample decays with a half-life of 14.3 days. What fraction remains after 28.6 days?

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

   Answer: 1/4

   Explanation: Two half-lives = 28.6 days. Remaining fraction = (1/2)² = 1/4. Option C miscalculates half-life count.

9. Question 9

   Q9. In beta-minus decay, a neutron converts to a proton via emission of a(n)...

   • A) electron and neutrino
   • B) positron and neutrino
   • C) electron and antineutrino
   • D) gamma photon

   Answer: electron and antineutrino

   Explanation: Beta-minus decay emits an electron and antineutrino. Option A incorrectly includes neutrino instead of antineutrino.

10. Question 10

    Q10. A fusion reaction releases 2.4 × 10¹⁵ J of energy. What mass was converted to energy? (c = 3 × 10⁸ m/s)

    • A) 26.7 g
    • B) 26.7 kg
    • C) 2.67 g
    • D) 0.267 kg

    Answer: 26.7 g

    Explanation: m = E/c² = 2.4 × 10¹⁵ / (9 × 10¹⁶) = 0.0267 kg = 26.7 g. Option B misplaces decimal.

11. Question 11

    Q11. The binding energy of ¹²C is 92.16 MeV. What is the average binding energy per nucleon?

    • A) 7.68 MeV
    • B) 12.0 MeV
    • C) 9.216 MeV
    • D) 23.04 MeV

    Answer: 7.68 MeV

    Explanation: Binding energy per nucleon = 92.16 MeV / 12 = 7.68 MeV. Option C divides by atomic number instead of mass number.

12. Question 12

    Q12. A ¹⁴C sample has 25% of its original activity. How many half-lives have passed?

    • A) 2
    • B) 3
    • C) 4
    • D) 1

    Answer: 2

    Explanation: Activity halves per half-life. 25% = (1/2)² = 2 half-lives. Option B miscalculates as three.

13. Question 13

    Q13. If a nucleus emits two alpha particles and one beta particle, what is the net change in atomic number?

    • A) -3
    • B) -1
    • C) -5
    • D) -2

    Answer: -3

    Explanation: Each alpha reduces atomic number by 2 (total -4), beta increases by 1. Net change = -3. Option D ignores beta decay.

14. Question 14

    Q14. A nuclear fission chain reaction requires a minimum mass of fissile material called the...?

    • A) critical mass
    • B) activation energy
    • C) binding energy
    • D) moderator weight

    Answer: critical mass

    Explanation: Critical mass is the minimum sustained fission. Option C confuses binding energy with mass requirement.

15. Question 15

    Q15. What is the energy equivalent of 1 atomic mass unit (u)? (1 u = 931 MeV/c²)

    • A) 931 MeV
    • B) 931 eV
    • C) 93.1 MeV
    • D) 9.31 MeV

    Answer: 931 MeV

    Explanation: 1 u = 931 MeV/c² by definition. Option B misuses decimal placement.

16. Question 16

    Q16. A ¹³¹I sample has a half-life of 8 days. What is its decay constant λ? (ln 2 ≈ 0.693)

    • A) 0.0866 day⁻¹
    • B) 0.693 day⁻¹
    • C) 8 day⁻¹
    • D) 0.00693 day⁻¹

    Answer: 0.0866 day⁻¹

    Explanation: λ = ln 2 / half-life = 0.693 / 8 = 0.0866 day⁻¹. Option D divides by 100 instead of 8.

17. Question 17

    Q17. A nucleus of uranium-238 undergoes alpha decay. What is the resulting nucleus?

    • A) Thorium-234
    • B) Radium-234
    • C) Actinium-234
    • D) Protactinium-234

    Answer: Thorium-234

    Explanation: U-238 alpha decay yields Th-234, as 2 protons and 2 neutrons are lost.

18. Question 18

    Q18. The binding energy per nucleon of deuterium is approximately 1.1 MeV. What is the total binding energy of the deuterium nucleus?

    • A) 1.1 MeV
    • B) 2.2 MeV
    • C) 3.3 MeV
    • D) 4.4 MeV

    Answer: 2.2 MeV

    Explanation: Deuterium has 2 nucleons, so 1.1 MeV/nucleon x 2 nucleons = 2.2 MeV total binding energy.

19. Question 19

    Q19. A neutron-induced fission reaction occurs in uranium-235. What is the average number of neutrons released per fission event?

    • A) 1.5
    • B) 2.5
    • C) 2.9
    • D) 3.5

    Answer: 2.9

    Explanation: U-235 fission releases approximately 2.9 neutrons per event, not 1.5, 2.5, or 3.5.

20. Question 20

    Q20. The half-life of a radioactive substance is 10 days. After 30 days, what fraction of the original sample remains?

    • A) 1/8
    • B) 1/4
    • C) 1/2
    • D) 3/4

    Answer: 1/8

    Explanation: After 3 half-lives, 1/2^3 = 1/8 of the sample remains, as each half-life reduces the sample by half.