In a radioactive material the activity at time t₁, is A₁ and at a later time t₂, it is A₂. If the decay constant of the material is $$\lambda$$, then

A proton has kinetic energy E = 100 eV which is equal to that of a photon. The wavelength of photon is $$\lambda$$₂ and that of proton is $$\lambda$$₁. The ratio $${{{\lambda _2}} \over {{\lambda _1}}}$$ is proportional to

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