In alpha particle scattering experiment, if $v$ is the initial velocity of the particle, then the distance of closest approach is $d$. If the velocity is doubled, then the distance of closest approach becomes

The ratio of area of first excited state to ground state of orbit of hydrogen atom is

The ratio of volume of $\mathrm{Al}^{27}$ nucleus to its surface area is (Given, $R_0=1.2 \times 10^{-15} \mathrm{~m}$)

Consider the nuclear fission reaction ${ }_0^1 n+{ }_{92}^{235} \mathrm{U} \longrightarrow{ }_{56}^{144} \mathrm{Ba}+{ }_{36}^{89} \mathrm{Kr}+3{ }_0^1 n$. Assuming all the kinetic energy is carried away by the fast neutrons only and total binding energies of ${ }_{92}^{235} \mathrm{U},{ }_{56}^{144} \mathrm{Ba}$ and ${ }_{36}^{89} \mathrm{Kr}$ to be $1800 \mathrm{MeV}, 1200$ MeV and 780 MeV respectively, the average kinetic energy carried by each fast neutron is (in MeV)