A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is :

(Assume that at t = 0, there are no B atoms in the sample)

There are 10¹⁰ radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $$\left( {\sqrt 2 = 1.414} \right)$$

At time t = 0, a material is composed of two radioactive atoms A and B, where N_A(0) = 2N_B(0). The decay constant of both kind of radioactive atoms is $$\lambda$$. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of N_B(t) / N_B(0) with respect to time t?

[N_A (0) = No. of A atoms at t = 0

N_B (0) = No. of B atoms at t = 0]

A particular hydrogen like ion emits radiation of frequency 2.92 $$\times$$ 10¹⁵ Hz when it makes transition from n = 3 to n = 1. The frequency in Hz of radiation emitted in transition from n = 2 to n = 1 will be :