Question

The work function of a metal is 1eV. On making light of wavelength $3000\mathring{A}$ incident on this metal, the velocity of photoelectrons emitted from it for photoelectric emission will be

• A. $2955km/s$
• B. $4200km/s$
• C. $1100km/s$
• D. $3000km/s$

Answer 1

Answer: (C)

The given answers are having the dimension of length [L]. It can be solvable.
The photo electric effect can be written as:

$E=\frac{m{v}^2}{2}+\varphi$

$\frac{m{v}^2}{2}=E-\varphi =\Delta E$

So, $v=\sqrt{[2\ast E/m)]}$
Now, the work function of a metal is $1eV=1.6\times {10}^{-19}$

And energy of the photon is $\frac{hc}{\lambda }=6.6\times {10}^{-19}$

So, $\Delta E=5.6\times {10}^{-19}$
Now the velocity of the photo electron is $v=\sqrt{[2\ast E/m)]}=1109053m/s=1100km/s$

So, the answer is option (C).