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321.
Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0, they have the same number of nuclei. The ratio of number of nuclei of A to that of B will be (1/e)² after a time interval of

$\frac{1}{λ}$

$\frac{1}{2 λ}$

$\frac{1}{3 λ}$

$\frac{1}{4 λ}$

$\frac{1}{2 λ}$

$We know that, N = N_{0} e^{- λt} For A, N_{A} = N_{0} e^{- 5 λt} For B, N_{B} = N_{0} e^{- λt} Given, \frac{N_{A}}{N_{B}} = \frac{1}{e^{2}} \frac{N}{N_{B}} = \frac{1}{e^{4 λt}} t = \frac{1}{2 λ}$

322.

The half-life of a radioactive isotope X is 20 yr. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

40 yr
60 yr
80 yr
100 yr

323.

A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)