Question

A small metal plate (work function =2eV) is placed at a distance of $2m$ from a monochromatic light source of wavelength $4.8\times {10}^{-7}$ m and power $1.0$ watt. The light falls normally on the plate. If a constant magnetic field of strength ${10}^{-4}$ T is applied parallel to the metal surface, then the radius of the largest circular path followed by the photo electrons is

• A. $2.56cm$
• B. $0.04cm$
• C. $0.04mm$
• D. $0.04km$

Answer 1

Answer: (A)

$2.56cm$

Energy possessed by each photon $=\frac{hc}{\lambda }$$=\frac{4.14\times {10}^{-15}\times 3\times {10}^8}{4.8\times {10}^{-7}}$$=2.5875eV$

Kinetic energy to the electron $=0.5875eV$

Let velocity of electron be $v_1$.
$\Rightarrow \frac{1}{2}\times m\times v{{}_1}^2=0.5875\times 1.6\times {10}^{-19}$
$V{{}_1}^2=\frac{{10}^{31-19}\times 0.5875\times 1.6\times 2}{9.1}$
$V_1=4.545\times {10}^{5}m/s$

So, radius in a magnetic field: $\frac{mv}{r}=BV$

$\frac{mv}{Bq}=\frac{9.1\times {10}^{-31}\times {10}^5\times 4.545}{{10}^{-4}\times {10}^{-19}\times 1.6}$$=0.0258m\approx 2.56cm$