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  • Electron beam used in an electron microscope, when accelerated by a voltage of 20kV, has a de − Broglie wavelength of <img alt="\lambda_0" src="https://entrancecorner.oncodecogs.com/gif.latex

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

Option: 1

3 \lambda_0


Option: 2

\frac{\lambda_0}{2}


Option: 3

\frac{\lambda_0}{\sqrt{2}}


Option: 4

9 \lambda_0


Answers (1)

best_answer

\begin{aligned} & \lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m K}}=\frac{h}{\sqrt{2 m e V}} \\ & \Rightarrow \lambda \alpha \frac{1}{\sqrt{V}} \\ & \Rightarrow \frac{\lambda_1}{\lambda_2}=\sqrt{\frac{V_2}{V_1}} \\ & \Rightarrow \frac{\lambda_0}{\lambda_2}=\sqrt{\frac{40}{20}}=\sqrt{2} \\ & \Rightarrow \lambda_2=\frac{\lambda_0}{\sqrt{2}} \end{aligned}

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Rishi

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