Electron beam when accelerated by a voltage of 10 kV, has a de-Broglie wavelength ' λ '. If the voltage is increased to 20 kV then the deBroglie wavelength associated with the electron beam would be (a) 4λ (b) 2λ (c) (λ)/(2) (d) (λ)/(√(2))

Answer: (d). λ = (h)/(√(2meV)) ⇒ λ ∝ 1/√(V). (λ')/(λ) = √(10/20) = 1/√(2). So the answer is (d) (λ)/(√(2)).

Electron beam when accelerated by a voltage of 10 kV, has a… | MHT CET 2025 (23 Apr, Shift 2)

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Matter Waves: de Broglie Wavelength

Electron beam when accelerated by a voltage of 10 kV, has a de-Broglie wavelength ' $\lambda$ '. If the voltage is increased to 20 kV then the deBroglie wavelength associated with the electron beam would be

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Answer: (d)

$\lambda = \dfrac{h}{\sqrt{2meV}} \Rightarrow \lambda \propto \dfrac{1}{\sqrt{V}}$ .
$\dfrac{\lambda'}{\lambda} = \sqrt{\dfrac{10}{20}} = \dfrac{1}{\sqrt{2}}$ .
So the answer is (d) $\dfrac{\lambda}{\sqrt{2}}$ .

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