The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is

A nucleus $${}_n^mX$$ emits one $$\alpha $$ particle and two $$\beta $$ particles. The resulting nucleus is

The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

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)