A photon emitted during the de-excitation of electron from a state $$\mathrm{n}$$ to the second excited state in a hydrogen atom, irradiates a metallic electrode of work function $$0.5 \mathrm{~eV}$$, in a photocell, with a stopping voltage of $$0.47 \mathrm{~V}$$. Obtain the value of quantum number of the state '$$n$$'.

A particle of mass $$2 \mathrm{mg}$$ has the same wavelength as a neutron moving with a velocity of $$3 \times 10^5 \mathrm{~ms}^{-1}$$. The velocity of the particle is (mass of neutron is $$1.67 \times 10^{-27} \mathrm{Kg}$$)

The threshold frequency for a metal surface is '$$n_0$$'. A photo electric current '$$I$$' is produced when it is exposed to a light of frequency $$\left(\frac{11}{6}\right) \mathrm{n}_{\mathrm{o}}$$ and intensity $$\mathrm{I}_{\mathrm{n}}$$. If both the frequency and intensity are halved, the new photoelectric current '$$\mathrm{I}^1$$' will become:

The mass of a particle $$\mathrm{A}$$ is double that of the particle $$\mathrm{B}$$ and the kinetic energy of $$\mathrm{B}$$ is $$\frac{1}{8}$$th that of A then the ratio of the de- Broglie wavelength of A to that of B is: