Question

An electron beam accelerated from rest through a potential difference of $5000V$ in vacuum is allowed to impinge on a surface normally. The incident current is $50\mu A$ and if the electron comes to rest on striking the surface, the force on it is

• A. $1.1924\times {10}^{-8}N$
• B. $2.1\times {10}^{-8}N$
• C. $1.6\times {10}^{-8}N$
• D. $1.6\times {10}^{-6}N$

Answer 1

The correct option is A $1.1924\times {10}^{-8}N$

Energy $=\frac{1}{2}m{v}^2=5000eV$
$=5000\times 1.6\times {10}^{-19}J$
$m{v}_2=\sqrt{2\times 5000\times (1.6\times {10}^{-19})}m$
$=4\times {10}^{-8}\sqrt{m}$
Number of electrons striking per second is
$n=\frac{q}{e}=\frac{It}{e}=\frac{50\times {10}^{-6}\times 1}{1.6\times {10}^{-19}}$
$\Rightarrow n=31.25\times {10}^{13}$
Force $=$ Change of momentum per second
$=n\left(mv\right)=31.25\times {10}^{13}\times 4\times {10}^{-8}\sqrt{m}$
$=125\times {10}^5\sqrt{9.1\times {10}^{-31}}=1.1924\times {10}^{-8}N$