Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV. has a de–Broglie wavelength of o. If the voltage is increased to 40 kV. then the de–Broglie wavelength associated with the electron beam would be
Select the correct option:
A
$3 \lambda_0$
B
$9 \lambda_0$
C
$\frac{\lambda_0}{2}$
D
$\frac{\lambda_0}{\sqrt{2}}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. When electron is accelerated through potential difference $V$, then K.E. $=\mathrm{eV}$
$$
\begin{array}{ll}
\Rightarrow & \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}(\mathrm{KE})}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{meV}}} \\
\therefore & \lambda \propto \frac{1}{\sqrt{\mathrm{~V}}} \\
\therefore & \frac{\lambda}{\lambda_0}=\sqrt{\frac{20}{40}} \\
\therefore & \lambda=\frac{\lambda_0}{\sqrt{2}}
\end{array}
$$
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