Write the expression for the de-Broglie wavelength associated with a charged particle having charge $q$ and mass $m$ , when it is accelerated by a potential $V$ .

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Solution

Let $v$ be the velocity gained by the given charged particle when it is accelerated through a potential difference of $V$ volts.
Kinetic energy of the particle = $\frac{1}{2} m v^{2}$ .
Kinetic energy of the particle = Work done on the particle by electric field.
$∴ \frac{1}{2} m v^{2} = q V$
or $\frac{P^{2}}{2 m} = q V$
$p =$ $\sqrt{2 m q V}$
de-Broglie wavelength $(λ)$ associated with the particle,
$λ = \frac{h}{p} = \frac{h}{\sqrt{2 m q V}}$

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Write the expression for the de-Broglie wavelength associated with a charged particle having charge q and mass m, when it is accelerated by a potential V.

Write the expression for the de-Broglie wavelength associated with a charged particle having charge $q$ and mass $m$ , when it is accelerated by a potential $V$ .