Two radioactive materials X₁ and X₂ have decay constants $$5\lambda $$ and $$\lambda $$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that X₂ will be 1/e after a time

The ground state energy of hydrogen atom is $$-$$ 13.6 eV. When its electron is in the first excited state, its excitation energy is

Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be

The total energy of electron in the ground state of hydrogen atom is $$-$$ 13.6 eV. The kinetic energy of an electron in the first excited state is