NTS NAT-IM (Medical / Pre-Medical Track) Physics Modern Physics — Set 2

NTS NAT-IM (Medical / Pre-Medical Track) Physics Modern Physics — Set 2

1. Question 1

   Q1. A photon of wavelength 400 nm is absorbed by a hydrogen atom. What is the energy of this photon?

   • A) 2.25 eV
   • B) 3.10 eV
   • C) 4.50 eV
   • D) 1.55 eV

   Answer: 3.10 eV

   Explanation: Energy = hc/λ = (6.63×10^-34 × 3×10^8)/(400×10^-9 × 1.6×10^-19) = 3.10 eV. Other options are incorrect calculations.

2. Question 2

   Q2. The half-life of a radioactive substance is 10 years. How much of a 100 g sample remains after 30 years?

   • A) 25 g
   • B) 12.5 g
   • C) 50 g
   • D) 6.25 g

   Answer: 12.5 g

   Explanation: After 30 years (3 half-lives), 100 g -> 50 g -> 25 g -> 12.5 g remains. Option C is after 1 half-life.

3. Question 3

   Q3. The mass defect of a nucleus is 0.01 u. What is the binding energy per nucleon if the nucleus has 20 nucleons?

   • A) 9.31 MeV
   • B) 4.65 MeV
   • C) 0.465 MeV
   • D) 46.5 MeV

   Answer: 0.465 MeV

   Explanation: Binding energy = 0.01 u × 931 MeV/u = 9.31 MeV. Per nucleon, it's 9.31/20 = 0.465 MeV. Other options miscalculate.

4. Question 4

   Q4. The work function of a metal is 2.5 eV. What is the maximum kinetic energy of electrons emitted when light of wavelength 300 nm shines on it?

   • A) 1.63 eV
   • B) 2.14 eV
   • C) 0.53 eV
   • D) 3.14 eV

   Answer: 2.14 eV

   Explanation: Photon energy = hc/λ = 4.14 eV. Max KE = 4.14 - 2.5 = 1.64 eV ≈ 1.63 eV (rounding).

5. Question 5

   Q5. A nucleus undergoes alpha decay. What is the change in its mass number?

   • A) -4
   • B) -2
   • C) 0
   • D) +2

   Answer: -4

   Explanation: Alpha decay emits a helium nucleus (2 protons, 2 neutrons), so mass number decreases by 4. Other options are incorrect changes.

6. Question 6

   Q6. The de Broglie wavelength of an electron moving at 10^6 m/s is approximately

   • A) 0.73 nm
   • B) 1.23 nm
   • C) 0.123 nm
   • D) 7.3 nm

   Answer: 0.73 nm

   Explanation: λ = h/mv = (6.63×10^-34)/(9.11×10^-31 × 10^6) = 0.73 nm. Other options miscalculate.

7. Question 7

   Q7. In a nuclear reaction, the mass defect is 0.05 u. What is the energy released?

   • A) 46.55 MeV
   • B) 46.5 MeV
   • C) 4.65 MeV
   • D) 0.465 MeV

   Answer: 46.55 MeV

   Explanation: Energy = 0.05 u × 931 MeV/u = 46.55 MeV. Other options are miscalculations or incorrect units.

8. Question 8

   Q8. The ionization energy of hydrogen is 13.6 eV. What is the energy required to ionize a hydrogen atom in the n=2 state?

   • A) 6.8 eV
   • B) 3.4 eV
   • C) 13.6 eV
   • D) 1.7 eV

   Answer: 3.4 eV

   Explanation: Energy of n=2 state = -13.6/4 = -3.4 eV. Ionization energy from this state is 3.4 eV. Other options misapply formulas.

9. Question 9

   Q9. A radioactive sample has a decay constant of 0.01 s^-1. What is its half-life?

   • A) 69.3 s
   • B) 100 s
   • C) 50 s
   • D) 200 s

   Answer: 69.3 s

   Explanation: Half-life = ln(2)/λ = 0.693/0.01 = 69.3 s. Other options miscalculate or use wrong formula.

10. Question 10

    Q10. The minimum energy required to eject an electron from a metal surface is 4.5 eV. What is the maximum wavelength of light that can eject an electron?

    • A) 275 nm
    • B) 300 nm
    • C) 250 nm
    • D) 325 nm

    Answer: 275 nm

    Explanation: λ = hc/E = (6.63×10^-34 × 3×10^8)/(4.5 × 1.6×10^-19) = 275 nm. Other options miscalculate or use wrong units.

11. Question 11

    Q11. The activity of a radioactive sample is 1000 Bq. If its half-life is 5 hours, what will be its activity after 10 hours?

    • A) 500 Bq
    • B) 250 Bq
    • C) 1000 Bq
    • D) 750 Bq

    Answer: 250 Bq

    Explanation: After 10 hours (2 half-lives), activity decreases from 1000 Bq to 500 Bq to 250 Bq. Other options are incorrect.

12. Question 12

    Q12. A proton and an electron have the same de Broglie wavelength. What is the ratio of their kinetic energies?

    • A) 1:1
    • B) 1:1836
    • C) 1836:1
    • D) 1:2000

    Answer: 1836:1

    Explanation: KE ∝ 1/m, so proton's KE is 1836 times electron's KE for the same λ. Other options miscalculate or ignore mass ratio.

13. Question 13

    Q13. The energy released in a nuclear fission reaction is 200 MeV. If 1 kg of fuel undergoes fission, what is the total energy released?

    • A) 8×10^13 J
    • B) 4×10^13 J
    • C) 1.6×10^14 J
    • D) 3.2×10^13 J

    Answer: 8×10^13 J

    Explanation: Number of nuclei in 1 kg = Avogadro's number × 1000/235 (approx.). Energy = 200 MeV × this number ≈ 8×10^13 J. Other options miscalculate.

14. Question 14

    Q14. The threshold wavelength for a metal is 500 nm. What is the work function of the metal?

    • A) 2.48 eV
    • B) 1.24 eV
    • C) 4.96 eV
    • D) 0.62 eV

    Answer: 2.48 eV

    Explanation: Work function = hc/λ = (6.63×10^-34 × 3×10^8)/(500×10^-9 × 1.6×10^-19) = 2.48 eV. Other options miscalculate.

15. Question 15

    Q15. A nucleus has a mass defect of 0.1 u. What is its binding energy?

    • A) 93.1 MeV
    • B) 93.1 eV
    • C) 46.55 MeV
    • D) 9.31 MeV

    Answer: 93.1 MeV

    Explanation: Binding energy = 0.1 u × 931 MeV/u = 93.1 MeV. Other options miscalculate or use wrong units.

16. Question 16

    Q16. The energy of the nth orbit of a hydrogen atom is -13.6/n^2 eV. What is the energy required to excite an electron from n=1 to n=3?

    • A) 12.09 eV
    • B) 10.2 eV
    • C) 13.6 eV
    • D) 1.51 eV

    Answer: 12.09 eV

    Explanation: ΔE = E3 - E1 = (-1.51) - (-13.6) = 12.09 eV. Other options miscalculate energy differences.

17. Question 17

    Q17. The half-life of radon is 3.8 days. How much of a 100 g sample remains after 11.4 days?

    • A) 25 g
    • B) 12.5 g
    • C) 50 g
    • D) 6.25 g

    Answer: 12.5 g

    Explanation: After 11.4 days (3 half-lives), 100 g -> 50 g -> 25 g -> 12.5 g remains. Other options are after fewer half-lives.

18. Question 18

    Q18. The decay constant of a radioactive substance is 0.05 min^-1. What is its half-life?

    • A) 13.86 min
    • B) 20 min
    • C) 10 min
    • D) 5 min

    Answer: 13.86 min

    Explanation: Half-life = ln(2)/λ = 0.693/0.05 = 13.86 min. Other options miscalculate or use wrong units.

19. Question 19

    Q19. The maximum kinetic energy of electrons emitted from a metal surface is 2 eV when light of frequency 6×10^14 Hz shines on it. What is the work function of the metal?

    • A) 1.2 eV
    • B) 0.8 eV
    • C) 0.48 eV
    • D) 1.52 eV

    Answer: 0.48 eV

    Explanation: Work function = hf - KE_max = (6.63×10^-34 × 6×10^14)/(1.6×10^-19) - 2 = 2.48 - 2 = 0.48 eV. Other options miscalculate.

20. Question 20

    Q20. A photon collides with a stationary electron. What is the minimum energy required for pair production?

    • A) 0.51 MeV
    • B) 1.02 MeV
    • C) 1.5 MeV
    • D) 2.04 MeV

    Answer: 1.02 MeV

    Explanation: Minimum energy = 2 × rest mass energy of electron = 2 × 0.51 MeV = 1.02 MeV. Other options are incorrect or miscalculated.