CONCEPT:

• Photonis an elementary particle whichsupplies energy to the electronsin a metal surface andby absorbingthisenergytheelectron comes out ofthemetal surface
• The rest mass of the photon iszero
• Proton is a positively charged nucleon
• The energy of an elementary particle in terms of wavelength can be written as

\(⇒ E = \frac{hc}{λ}\)

Where h = Plancks constant andλ = Wavelength

• The wavelength of an electroncan be written as

\(λ =\frac{h}{\sqrt{2ME}}\)

Where h = Plancks constant, M = mass of the proton, E = kinetic energy

EXPLANATION :

• The wavelength of an electron can be written as

\(⇒ λ _{e}=\frac{h}{\sqrt{2M_{e}E}}\)----(1)

• The energy of an elementary photonin terms of wavelength can be written as

\(⇒ E = \frac{hc}{λ_{p}}\)------(2)

Squaring equation 1 and substituting the value E from equation 2 to equation 1 (Since both the particle has the same energy)

\(⇒ \lambda^{2}_{e} = \frac{h^{2}}{2M_{e}\frac{hC}{\lambda_{P}}}\)

\(\Rightarrow \lambda_{e}^{2} = \frac{h^{2}\times \lambda_{P}}{2M_e hC}\)

The above equation can be written as

\(\Rightarrow \lambda_{e}^{2} \propto \lambda_{P}\)

• Hence, option 4 is the answer