Question

The wavelength of electrons accelerated from rest through a potential difference of $40\, kV$ is $x \times 10^{-12} m$. The value of $x$ is _______ (Nearest integer)
Given : Mass of electron $=9.1 \times 10^{-31} kg$
Charge on an electron $=1.6 \times 10^{-19} C$
Planck's constant $=6.63 \times 10^{-34} JS$

Answer 1

De-broglie-wave length of electron:
$\lambda_{e}=\frac{h}{\sqrt{2 m(K E)}}$
$\left\{\because e^{-}\right.$is accelerated from rest $\Rightarrow K E=q \times V$
$\lambda =\frac{h}{\sqrt{2 m q v}} $
$=\frac{6.63 \times 10^{-34}}{\sqrt{2 \times 1.6 \times 10^{-19} \times 9.1 \times 10^{-31} \times 40 \times 10^{3}}}$
$=0.614 \times 10^{-11} m $
$=6.14 \times 10^{-12} m$
Nearest integer $=6$