Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of . If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be [2023]

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Solution

Q.
Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $λ_{0}$ . If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be [2023]

1 $\frac{λ_{0}}{2}$

2 $3 λ_{0}$

3 $\frac{λ_{0}}{\sqrt{2}}$

4 $9 λ_{0}$

Ans.
(3)

$λ = \frac{h}{\sqrt{2 m V q}}$

$\frac{λ}{λ_{0}} = \sqrt{\frac{20}{40}} \Rightarrow λ = \frac{λ_{0}}{\sqrt{2}}$

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