The eyes of certain member of the reptile family pass a single visual signal to the brain when the visual receptors are struck by photons of wavelength $850 \mathrm{nm}.$ If a total energy of $3.15\times {10}^{-14} \mathrm{J}$ is required to trip the signal, if minimum number of photons that must strike the receptor is $\mathrm{y}\times {10}^3$ then find value of $\mathrm{y}.$(Round off your answer to the nearest integer.

Given: Planck's constant $=6.62\times {10}^{-34}\mathrm{Js}$

A metal was irradiated by light of frequency $3.2\times {10}^{15}{ \mathrm{s}}^{-1}.$ The photoelectron produced had its kinetic energy $2$ times of  the kinetic energy of the photoelectron which was produced when the same metal was irradiated with a light of frequency $2.0\times {10}^{15}{ \mathrm{s}}^{-1}.$ What is work function of the metal $\left(\mathrm{kJ}/\mathrm{mol}\right) ?$

Given: Planck's constant: $6.62\times {10}^{-34}\mathrm{Js}$, Avogadro's number: $6.02\times {10}^{23}$

Round off your answer to the nearest integer.

A potential difference of $20 \mathrm{kV}$ is applied across an $\mathrm{X}$-ray tube. The minimum wavelength (in $\stackrel{\circ }{\mathrm{A}}$) of $\mathrm{X}$-ray generated is $\frac{\mathrm{a}}{100}$. The value of $\mathrm{a}$ is

Given: Planck's constant: $6.626\times {10}^{-34}\mathrm{Js}$

Round of the answer to the nearest integer.