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 :

Consider the following statements :

A. Atoms of each element emit characteristics spectrum.

B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.

C. The density of nuclear matter depends on the size of the nucleus.

D. A free neutron is stable but a free proton decay is possible.

E. Radioactivity is an indication of the instability of nuclei.

Choose the correct answer from the options given below :

If 'f' denotes the ratio of the number of nuclei decayed (N_d) to the number of nuclei at t = 0 (N₀) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as :

[$$\lambda$$ is the radioactive decay constant]

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :

(where $$\lambda$$ is the decay constant)