When a metal surface is irradiated with light of wavelength $4950\stackrel{\circ }{A}$, a photo current appears. This photo current vanishes, if a retarding potential greater than $0.6$ volt is applied across the photo tube. However, when a different source of light is used, it is found that the critical retarding potential is changed to 1.1 volt. Calculate the work function of the emitting metal surface and the wavelength of second source. If the photo electrons (after emission from the surface) are subjected to a magnetic field of 10 Tesla, what changes will be observed in the above two retarding potentials.

In the first case, energy of incident photon in $eV$ is

$E_1=\frac{12375}{4950}eV=2.5eV$

The maximum kinetic energy of ejected electrons is

${\left(K_{\max }\right)}_1=e{V}_1=0.6eV$

According to Einstein's photo electric equation, we have

$E={\varphi }_0+K_{\max }$

$\Rightarrow {\varphi }_0=E_1-{\left(K_{\max }\right)}_1$

$\Rightarrow {\varphi }_0=(2.5-0.6)eV=1.9eV$

In second case, the maximum kinetic energy of ejected electrons is

${\left(K_{\max }\right)}_2=e{V}_2=1.1eV$

According to Einstein's photo electric equation, we have

$E={\varphi }_0+K_{\max }$

$\Rightarrow E_2=(1.9+1.1)eV=3.0eV$

So, the wavelength of incident photons in second case

${\lambda }_2=\frac{12375}{3.0}Å=4125Å$

Since work done by magnetic force in moving charged particle is zero, a magnetic field cannot speed up or slow down a charged particle, and therefore there will be no effect on the stopping potential because the kinetic energy of the emitted photoelectrons remains the same.