If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength (λ) associated with the electrons change? (a) λ is increased to √(2) times. (b) λ is increased to 1/√(2) times. (c) λ is decreased to 1/√(2) times. (d) λ is decreased to √(2) times.

Answer: (c). λ ∝ 1/√(V). V' = 2V ⇒ λ' = (λ)/(√(2)), a decrease. So the answer is (c) λ is decreased to 1/√(2) times.

If the potential difference used to accelerate electrons is doubled… | MHT CET 2024 (11 May, Shift 1)

Q51MHT CET 2024 · 11 MAY · SHIFT 1Easy

Matter Waves: de Broglie Wavelength

If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength $(\lambda)$ associated with the electrons change?

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Answer: (c)

$\lambda \propto \dfrac{1}{\sqrt{V}}$ .
$V' = 2V \Rightarrow \lambda' = \dfrac{\lambda}{\sqrt{2}}$ , a decrease.
So the answer is (c) $\lambda$ is decreased to $\dfrac{1}{\sqrt{2}}$ times.

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