StudentAidUnit 19: Nuclear and Particle Physics — Numericals
12th Class Physics · Unit 19: Nuclear and Particle Physics
CR-19.4.A source has an activity of 10 × 10⁴ Bq and a half-life of 20 minutes. What will be the activity of the source after one hour?
Given
A₀ = 10 × 10⁴ Bq = 1 × 10⁵ Bq, T½ = 20 min, t = 1 hour = 60 min.
Number of half-lives, n = t/T½ = 60/20 = 3.
Formula: A = A₀(1/2)ⁿ
A = 1 × 10⁵ × (1/2)³ = 1 × 10⁵ × (1/8)
A = 1.25 × 10⁴ Bq.
NUM-19.1.Find the mass defect and binding energy of the deuterium. The mass of deuteron is 3.3435 × 10⁻²⁷ kg. (Mass of proton mₚ = 1.6726 × 10⁻²⁷ kg, mass of neutron mₙ = 1.6749 × 10⁻²⁷ kg) (Book answer: 2.23 MeV)
NUM-19.2.The decay constant of strontium is 1.99 × 10⁻⁵ s⁻¹. Find its half-life. (Book answer: 9.7 hours)
Given
λ = 1.99 × 10⁻⁵ s⁻¹.
Formula: T½ = 0.693/λ
T½ = 0.693/(1.99 × 10⁻⁵) = 34824 s.
Converting to hours: T½ = 34824/3600 ≈ 9.67 h ≈ 9.7 hours.
NUM-19.3.Half-life of krypton is 3.16 minutes. Out of 40 g of krypton, how much will be left after 12.64 minutes? (Book answer: 2.5 g)
Given
T½ = 3.16 min, t = 12.64 min, initial mass = 40 g.
Number of half-lives: n = t/T½ = 12.64/3.16 = 4.
Remaining mass: m = m₀(1/2)ⁿ = 40 × (1/2)⁴ = 40/16
m = 2.5 g.
NUM-19.4.32 g sample of a radioactive material remain after 18 years. What is its half-life? (Book answer: 3 years)
NUM-19.5.An alpha particle has an energy of 5.56 MeV when released from the radium atom. Determine its velocity. (Book answer: 1.68 × 10⁷ m s⁻¹)
NUM-19.6.Find the energy released during the nuclear reaction: ⁷₃Li + ¹₁H → 2 ⁴₂He. Mass of ⁴₂He = 4.00388 u, ¹₁H = 1.00814 u and of ⁷₃Li = 7.01823 u. (Book answer: 19.2 MeV)