Question

A filter transmits only the radiation of wavelength greater than 440 nm. Radiation from a hydrogen-discharge tube goes through such a filter and is incident on a metal of work function 2.0 eV. Find the stopping potential which can stop the photoelectrons.

Answer 1

Wavelength of radiation coming from filter, λ = 440 nm
Work function of metal, ϕ = 2 eV
Charge of the electron​, e = 1.6 $\times$ 10^$-9$ C
Let V₀ be the stopping potential.
From Einstein's photoelectric equation,
$\frac{hc}{\mathrm{\lambda }}-\varphi =e{V}_0$
Here,
h =Planck constant
c = Speed of light
$\lambda$ = Wavelength of radiation

$$\begin{gathered} \frac{4.14\times {10}^{-15}\times 3\times {10}^8}{440\times {10}^{-9}}-2\mathrm{eV}={\mathrm{eV}}_0 \\ \Rightarrow e{V}_0=\left(\frac{1242}{440}-2\right)\mathrm{eV}=0.823\mathrm{eV}. \\ \Rightarrow V_0=0.823\mathrm{Volts} \end{gathered}$$