The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to [2023]

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Solution

Q.
The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is proportional to [2023]

1 $\frac{1}{\sqrt{V}}$

2 $V^{2}$

3 $\sqrt{V}$

4 $\frac{1}{V}$

Ans.
(4)

Energy of X-ray = $h υ = \frac{h c}{λ}$

As K.E is maximum, thus $λ$ is minimum.

So, energy of emitted X-ray = energy of electron

$\frac{h c}{λ_{\min}} = e V \Rightarrow λ_{\min} = \frac{h c}{e} \times \frac{1}{V} \Rightarrow λ_{\min} \propto \frac{1}{V}$

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