The radius of a muonic hydrogen atom is 2.5 $$\times$$ 10^$$-$$13 m. The total atomic volume (in m³) of a mole of such hydrogen atoms is (Take, $$\pi$$ = 3.14)

A radioactive sample at any instant has its disintegration rate 5000 disintegrations per min. After 5 min, the rate is 1250 disintegrations per min. Then, the disintegration constant (per min) is

Identify the hydrogen-like element whose spectral lines are four times shorter in wavelength compared to those of atomic hydrogen.

The decay constants of two radioactive substances X and Y are 4$$\lambda$$ and $$\lambda$$ respectively. At t = 0, a sample has the same number of two nuclei. The time taken for the ratio of number of nuclei to become $${1 \over {{e^3}}}$$ will be