A light of energy $$12.75 ~\mathrm{eV}$$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $$\frac{x}{\pi} \times 10^{-17} ~\mathrm{eVs}$$. The value of $$x$$ is ___________ (use $$h=4.14 \times 10^{-15} ~\mathrm{eVs}, c=3 \times 10^{8} \mathrm{~ms}^{-1}$$ ).

For hydrogen atom, $$\lambda_{1}$$ and $$\lambda_{2}$$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $$\lambda_{1}$$ and $$\lambda_{2}$$ is $$\frac{x}{32}$$. The value of $$x$$ is __________.

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \mathrm{~s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11} \mathrm{~s}$. The value of $\alpha$ is __________.