A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C¹⁴ is 5730 years, then age of the wooden piece placed in the museum is approximately :

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV . The ratio of energies of $\alpha$-rays produced by A and B is $\_\_\_\_$ .

The energy released if hydrogen atoms are combined to form ${ }_2^4 \mathrm{He}$ is $\_\_\_\_$ MeV .

(Take binding energies per nucleon of ${ }_1^2 \mathrm{H}$ and ${ }_2^4 \mathrm{He}$ as 1.1 MeV and 7.2 MeV , respectively)

The ratio of momentum of the photons of the $1^{\text {st }}$ and $2^{\text {nd }}$ line of Balmer series of Hydrogen atoms is $\alpha / \beta$. The possible values of $\alpha$ and $\beta$ are:-