Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively. Initially, the samples have equal number of nuclei. After 80 minutes, the ratio of decayed numbers of A and B nuclei will be:

• 1: 16

• 4 : 1

• 1: 4

• 1: 4

Proton, Deuteron and alpha particle of the same kinetic energy is moving in circular trajectories in a constant magnetic field. The radii of the proton, deuteron and alpha particle are respectively r_p, r_d and r_α. Which one of the following relations is correct?

•  r_α = r_p= r_d

•  r_α = r_p< r_d

•  r_α > r_d> r_p

•  r_α > r_d> r_p

Assume that a neutron breaks into a proton and an electron. The energy released during this process is(Mass of neutron = 1.6725 x 10^–27kg; mass of proton = 1.6725 x 10^–27kg; mass of electron = 9 x 10^–31kg)

• 0.73 MeV

• 7.10 MeV

• 6.30 MeV

• 6.30 MeV

The half life of a radioactive substance is 20 minutes. The approximate time interval (t₂ - t₁) between the time t₂ when 2/3 of it has decayed and time t₁ when 1/3 of it had decayed is

• 14 min

• 20 min

• 28 min

• 28 min

A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M/2 each. The speed of light is c.
The binding energy per nucleon for the parent nucleus is E₁ and that for the daughter nuclei is E₂. Then

• E₁ = 2E₂

• E₂ = 2E₁

• E₁ > E₂

• E₁ > E₂

A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c.

The speed of daughter nuclei is

A radioactive nucleus (initial mass number A and atomic number Z) emits 3 α–particles and 2 positions. The ratio of number of neutrons to that of protons in the final nucleus will be

A radioactive nucleus A with a half-life T, decays into a nucleus B. At t = 0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3. Then, t is given by

• t = T log (1.3)

• 
• 
• 

The above is a plot of binding energy per nucleon Eb, against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions:

(i) A + B → C + ε  (ii) C → A + B + ε
(iii) D + E → F + ε and (iv) F → D + E +ε

where ε is the energy released? In which reaction is ε positive?

• (i) and (iv)

• (i) and (iii)

• (ii) and (iv)

• (ii) and (iv)

The transition from the state n = 4 to n = 3 in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

• 2 → 1

• 3 → 2

• 4 → 2

• 4 → 2