Question

Light of wavelength 180 nm ejects photoelectrons from a plate of a metal whose work function is $2eV$. If a uniform magnetic field of $5\times {10}^{-5}$ T is applied parallel to the plate, what would be the radius of the path followed by electrons ejected normally from the plate with maximum energy :

• A. $0.228m$
• B. $0.448m$
• C. $0.748m$
• D. $0.148m$

Answer 1

The correct option is D $0.148m$

Energy of incident photon $E_{incident}=\frac{1240}{\lambda \left(innm\right)}eV$

$⟹E_{incident}=\frac{1240}{180}=6.9eV$

Maximum kinetic energy of photo electrons $K.E_{max}=E_{incident}-\varphi$

where $\varphi$ is the work function of metal.

$\therefore$ $K.E_{max}=6.9-2=4.9eV$

Maximum momentum of the electron $P=mv=\sqrt{2mK.E_{max}}$

$\therefore$ $mv=\sqrt{2\times 9.1\times {10}^{-31}\times 4.9\times 1.6\times {10}^{-19}}=1.2\times {10}^{-24}kg.m/s$

Radius of circular path $R=\frac{mv}{eB}$

where $B=5\times {10}^{-5}T$

$⟹R=\frac{1.2\times {10}^{-24}}{1.6\times {10}^{-19}\times 5\times {10}^{-5}}=0.148m$