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

Wavelength $\left(\lambda \right)$of electron is given by
$\lambda =\frac{h}{\sqrt{2mqV}}$
Here
$h\text{is planck's constant}$
$m\text{is mass of electron}$
$q\text{is harge on electron}$
$V\text{is potential difference}$

Putting the values:
$\lambda =\frac{6.63\times {10}^{-34}}{\sqrt{2\times 9.1\times {10}^{-31}\times 1.6\times {10}^{-19}\times 40\times {10}^3}}$

$=\frac{6.63\times {10}^{-34}}{\sqrt{116.48\times {10}^{-46}}}=6.144\times {10}^{-12}=6\times {10}^{-12}$

$x=6$