In a biprism experiment, the distance between $4^{th}$ and $13^{th}$ bright band on the same side is '$y$' when light of wavelength $6000$ Å is used. For a light of wavelength '$\lambda$' the distance between $6^{th}$ and $16^{th}$ bright band on the same side is again '$y$'. The value of '$\lambda$' in Å units is

The proton and $\alpha$ - particle are accelerated through same potential difference. Then the ratio of the de-Broglie wavelength of proton and $\alpha$ - particle is (mass of $\alpha$-particle is $4$ times mass of proton, charge of $\alpha$-particle is $2$ times charge of proton)

Two identical photocathodes receive light of frequencies $n_1$ and $n_2$. If the velocities of the emitted photoelectrons of mass m are $V_1$ and $V_2$ respectively, then ($h$ = Planck's constant)

An electron in the hydrogen atom jumps from $n^{th}$ energy state to the ground state. The wavelength so emitted illuminates a photosensitive material having work function $2.65$ eV. If the maximum kinetic energy of the emitted photoelectrons is $10.1$ eV, then the value of '$n$' is