Question 127: Dual Nature of Matter and Radiation

Question

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $$\lambda_0$$. IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :

Accepted Answer

When electron is accelerated through potential difference $V$, then
$$
\begin{aligned}
& 	ext { K.E. }=\mathrm{eV} \\
& \Rightarrow \lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}(\mathrm{KE})}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{meV}}} \\
& 	herefore \lambda \alpha \frac{1}{\sqrt{\mathrm{V}}} \\
& 	herefore \frac{\lambda}{\lambda_0}=\sqrt{\frac{20}{40}} \\
& 	herefore \lambda=\frac{\lambda_0}{\sqrt{2}}
\end{aligned}
$$

Answer

3 $$\lambda_0$$

Answer

9 $$\lambda_0$$

Answer

$$\frac{\lambda_0}{\sqrt2}$$

Answer

$$\frac{\lambda_0}{2}$$

Dual Nature of Matter and Radiation

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $\lambda_0$. IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :

Choose the correct answer: