The decay constant of a radio isotope is $$\lambda $$. If A₁ and A₂ are its activities at times t₁ and t₂ respectively, the number of nuclei which have decayed during the time (t₁ $$-$$ t₂)

An alpha nucleus of energy $${1 \over 2}$$ mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to

The activity of a radioactive sample is measured as N₀ counts per minute at t = 0 and N₀/e counts per minute at t = 5 minutes. The time (in minutes) at which the activity reduces to half its value is

The energy of a hydrogen atom in the ground state is $$-$$ 13.6 eV. The energy of a He⁺ ion in the first excited state will be