Energy required for the electron excitation in $$L{i^{ + + }}$$ from the first to the third Bohr orbit is :

The half life of a radioactive substance is $$20$$ minutes. The approximate time interval $$\left( {{t_2} - {t_1}} \right)$$ between the time $${{t_2}}$$ when $${2 \over 3}$$ of it had decayed and time $${{t_1}}$$ when $${1 \over 3}$$ of it had decayed is :

A nucleus of mass $$M+$$$$\Delta m$$ is at rest and decays into two daughter nuclei of equal mass $${M \over 2}$$ each. Speed of light is $$c.$$

The binding energy per nucleon for the parent nucleus is $${E_1}$$ and that for the daughter nuclei is $${E_2}.$$ Then

A radioactive nucleus (initial mass number $$A$$ and atomic number $$Z$$ emits $$3\,\alpha $$- particles and $$2$$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be