Physics - Modern Physics Question with Solution | TestHub

The correct option is (B). Concept: Einstien's Photoelectric effect theory The maximum kinetic energy $\mathrm{K}$ of the photoelectric electrons is related to the incident wavelength $\lambda$ and work function $\varphi$ of the metal as follows: $\mathrm{K}=\frac{\mathrm{hc}}{\lambda }-\varphi$ For the incident wavelength $\lambda$, the equation is $\mathrm{K}=\frac{\mathrm{hc}}{\lambda }-\varphi$ And for the incident wavelength $\frac{\lambda }{2}$, the equation is $3K=\frac{\mathrm{hc}}{\frac{\lambda }{2}}-\varphi$ Taking the ratio of two equations: $\frac{1}{3}=\frac{\left(\frac{\mathrm{hc}}{\lambda }-\varphi \right)}{\left(\frac{\mathrm{hc}}{\frac{\lambda }{2}}-\varphi \right)}$ On solving, we get $\varphi =\frac{\mathrm{hc}}{2\lambda }$