A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be $${\left( {{x \over 3}} \right)^{{1 \over 3}}}$$. The value of '$$x$$' is :-

The wavelength of the radiation emitted is $$\lambda_0$$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will $$\frac{20}{x}\lambda_0$$. The value of $$x$$ is _____________.

The energy released per fission of nucleus of $$^{240}$$X is 200 MeV. The energy released if all the atoms in 120g of pure $$^{240}$$X undergo fission is ____________ $$\times$$ 10$$^{25}$$ MeV.

(Given $$\mathrm{N_A=6\times10^{23}}$$)

Assume that protons and neutrons have equal masses. Mass of a nucleon is $$1.6\times10^{-27}$$ kg and radius of nucleus is $$1.5\times10^{-15}~\mathrm{A^{1/3}}$$ m. The approximate ratio of the nuclear density and water density is $$n\times10^{13}$$. The value of $$n$$ is __________.