A hydrogen atom in ground state is given an energy of $$10.2 \mathrm{~eV}$$. How many spectral lines will be emitted due to transition of electrons?

A proton and a deutron $$(q=+\mathrm{e}, m=2.0 \mathrm{u})$$ having same kinetic energies enter a region of uniform magnetic field $$\vec{B}$$, moving perpendicular to $$\vec{B}$$. The ratio of the radius $$r_d$$ of deutron path to the radius $$r_p$$ of the proton path is:

The temperature of a gas is $$-78^{\circ} \mathrm{C}$$ and the average translational kinetic energy of its molecules is $$\mathrm{K}$$. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes $$2 \mathrm{~K}$$ is :

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is: