The kinetic energy of an electron is tripled, then the de-Broglie wavelength associated with it, will change…
The kinetic energy of an electron is tripled, then the de-Broglie wavelength associated with it, will change by a factor
$\frac{1}{3}$
$3$
$\sqrt{3}$
$\frac{1}{\sqrt{3}}$
Solution
de-Broglie wavelength of an electron $\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mK}}}$ Or $\lambda \propto \frac{1}{\sqrt{\mathrm{K}}}$
where $\mathrm{K}$ is the kinetic energy of the electron and $\mathrm{m}$ is the mass.
$\begin{aligned}
& \therefore \frac{\lambda^{\prime}}{\lambda}=\frac{1}{\sqrt{3^{\mathrm{K}}}} \cdot \frac{\sqrt{\mathrm{K}}}{1}=\frac{1}{\sqrt{3}} \\
& \text { Or } \lambda^{\prime}=\frac{\lambda}{\sqrt{3}}
\end{aligned}$
i.e., de-Broglie wavelength will decrease by a factor of $\frac{1}{\sqrt{3}}$.
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