Time taken by light to travel in two different materials $$A$$ and $$B$$ of refractive indices $$\mu_{A}$$ and $$\mu_{B}$$ of same thickness is $$t_{1}$$ and $$t_{2}$$ respectively. If $$t_{2}-t_{1}=5 \times 10^{-10}$$ s and the ratio of $$\mu_{A}$$ to $$\mu_{B}$$ is $$1: 2$$. Then, the thickness of material, in meter is: (Given $$v_{\mathrm{A}}$$ and $$v_{\mathrm{B}}$$ are velocities of light in $$A$$ and $$B$$ materials respectively.)

A metal exposed to light of wavelength $$800 \mathrm{~nm}$$ and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength $$500 \mathrm{~nm}$$ is used. The workfunction of the metal is : (Take hc $$=1230 \,\mathrm{eV}-\mathrm{nm}$$ ).

The momentum of an electron revolving in $$\mathrm{n}^{\text {th }}$$ orbit is given by :

(Symbols have their usual meanings)

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :