Modern physics test

NUCLEAR PHYSICS – Chapter Test

Marking Scheme: +4 for correct answer, -1 for incorrect, 0 for no response.

Section A – Physics Single Correct (20 MCQs)

Q1. When aluminium is bombarded with fast neutrons:
₁₃Al²⁷ + n → ₁₁Na²⁴ + x
What is x?

Electron Proton Neutron Alpha particle

Q2. The binding energies per nucleon for ₁H² and ₂He⁴ are 1.1 MeV and 7.1 MeV respectively.
The energy released when two hydrogen nuclei fuse to form helium is:

4.4 MeV 8.2 MeV 24 MeV 28.4 MeV

Q3. A carbon nucleus emits a particle x and changes into nitrogen:
₆C¹⁴ → ₇N¹⁴ + x
What is x?

Electron Proton Alpha particle Photon

Q4. The binding energy per nucleon of C–12 is 7.68 MeV and that of C–13 is 7.48 MeV.
The energy required to remove the extra neutron from C–13 is nearly:

0.2 MeV 3.7 MeV 3.9 MeV 5 MeV

Q5. A radioactive source of half-life 2 h emits radiation of intensity 64× the safe level.
Minimum time to work safely is:

6 h 12 h 24 h 128 h

Q6. The activity of a radioactive element reduces to ¹/₁₆ of its initial value in 36 years.
The half-life is:

6 years 9 years 12 years 18 years

Q7. The transition n=4 → n=3 in a hydrogen-like atom gives UV radiation.
Infrared radiation will be from:

2 → 1 3 → 2 4 → 2 5 → 4

Q8. A nucleus with A = 208 emits an alpha particle (energy = E). The energy of disintegration is:

52E/51 51E/52 52E E

Q9. If the radius of _X²⁵⁶ is 8 fermi, the radius of ₂He⁴ is:

1 fermi 2 fermi 3 fermi 4 fermi

Q10. The binding energy of deuteron is 1.15 MeV/nucleon and that of alpha particle is 7.1 MeV/nucleon.
In the reaction: ₁H² + ₁H² → ₂He⁴ + Q
What is Q?

1 MeV 11.9 MeV 23.8 MeV 931 MeV

Q11. A star has 10⁴⁰ deuterons and radiates 10¹⁶ W through:
₁H² + ₁H² → ₁H³ + p, ₁H³ + ₁H² → ₂He⁴ + n
Given masses: m(₁H²)=2.014u, m(p)=1.007u, m(n)=1.008u, m(₂He⁴)=4.001u
Exhaustion time is of the order:

10⁶ s 10⁸ s 10¹² s 10¹⁶ s

Q12. During negative beta decay:

Atomic electron is ejected Pre-existing nuclear electron is ejected Neutron decays into proton + electron Binding energy is converted into an electron

Q13. Radioactivity of a sample is X at t₁ and Y at t₂, mean life = τ. Disintegrated atoms in (t₂ - t₁) is:

Xt₁ - Yt₂ X - Y (X - Y)/τ (X - Y)τ

Q14. A nucleus splits into two parts with radii ratio 1:2.
Velocity ratio is:

8:1 6:1 4:1 2:1

Q15. Fission of one uranium atom releases 200 MeV.
Number of fissions/s to get 3.2 W is:

10⁷ 10¹⁰ 10¹⁵ 10¹¹

Q16. Activity of sample = 4×10¹⁰ dis/sec, mean life = 10³ s, atomic mass = 10^-25 kg.
Mass of sample is:

1 mg 2 mg 4 mg 8 mg

Q17. Half-life of ₅₃I¹³¹ = 8 days.
Claim:

No nucleus decays before 4 days No nucleus decays before 8 days All nuclei decay before 16 days Any nucleus may decay anytime after t=0

Q18. Two radioactive materials X₁ and X₂ have λ₁ = 10λ₂ = 10λ and λ₂ = λ. Initially same nuclei count. Ratio N₁/N₂ = 1/e after time:

1/10λ 1/11λ 1/9λ None of these

Q19. After 2 h, 1/16 fraction of isotope remains.
Half-life is:

15 min 30 min 45 min 1 hour

Q20. Electron in beta radiation comes from:

Inner atomic orbits Free electrons in nuclei Decay of neutron in nucleus Escaping photon

Section B – Physics Numerical (5 Numerical Questions)

Q21. Activity of sample A = 0.5 × activity of sample B, but sample A has twice the number of nuclei of B.
Find the ratio T_1/2(A) : T_1/2(B):

Q22. In H atom, orbital radius in state n₁ is 4× that in n₂.
Find n₁/n₂:

Q23. Half-life = 20 min.
Find time interval between 33% decay and 67% decay (Give T/10):

Q24. Ground state H radius = 0.53 Å. Collision excites electron to orbit of radius 4.77 Å.
Find principal quantum number of final state:

Q25. Half-life = 6.93 days.
When will 1/20th remain? (Take ln 20 = 3.0) (Answer in months):