Question

de Broglie wavelength of charged particles depends on:

• A. All above
• B. Nature of particle
• C. Kinetic energy of particle
• D. Mass of particle

Answer 1

The correct option is A All above

de Brogie wavelength $\left(\lambda \right)=\frac{h}{mv}$
Where:
$\lambda =\text{de Broglie wavelength}$
$h\text{(Plank's constant)}=6.626\times {10}^{-34}\text{J s}$
$m=\text{Mass}$
$v=\text{Velocity}$
$\text{Kinetic energy}\left(E\right)=\frac{1}{2}m{v}^2$
$\Rightarrow v=\sqrt{\frac{2E}{m}}$
$\Rightarrow \lambda =\frac{h}{\sqrt{2mE}}$
$\Rightarrow \text{For charged particle energy},E=q\times V$
Where,
$q=\text{charge on the particle}$
$V=\text{Potential}$
$\Rightarrow \lambda =\frac{h}{\sqrt{2mqV}}$