Question

An electron of charge 'e' and mass 'm' is accelerated from rest by a potential difference 'V'. The de Broglie wavelength is

• A. Directly proportional to the square root of potential difference.
• B. Inversely proportional to the square root of potential difference
• C. Directly proportional to the square root of electron mass
• D. Inversely proportional to the cube root of electron mass

Answer 1

The correct option is B Inversely proportional to the square root of potential difference

$\frac{1}{2}m{v}^2=eV$
$mv=\sqrt{2eVm}$
So de-broglie wavelength
$\lambda =\frac{h}{mv}$
$=\frac{h}{\sqrt{2meV}}$
$\therefore \lambda \alpha \frac{1}{\sqrt{V}}$