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

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

A diatomic molecule has moment of inertia ' I ', By applying Bohr's quantization condition, its rotational energy in the $\mathrm{n}^{\text {th }}$ level is $[\mathrm{n} \geq 1]$ [h= Planck's constant]

In the uranium radioactive series, the initial nucleus is ${ }_{92}^{238} \mathrm{U}$ and that the final nucleus is ${ }_{82}^{206} \mathrm{~Pb}$. When uranium nucleus decays into lead, the number of $\alpha$-particles and $\beta$-particles emitted are