The de Broglie wavelength of an electron having kinetic energy E is λ. If the kinetic energy of electron becomes E/4, then its de-Broglie wavelength will be: (a) √(2)λ (b) 2λ (c) (λ)/(2) (d) (λ)/(√(2))

Answer: (b). λ ∝ 1/√(E). E' = E/4 ⇒ λ' = λ√(4) = 2λ. So the answer is (b) 2λ.

The de Broglie wavelength of an electron having kinetic energy E is… | JEE Main 2023 (15 Apr, Shift 1)

Q63JEE Main 2023 · 15 APR · SHIFT 1Easy

Matter Waves: de Broglie Wavelength

The de Broglie wavelength of an electron having kinetic energy $\mathrm{E}$ is $\lambda$ . If the kinetic energy of electron becomes $\frac{E}{4}$ , then its de-Broglie wavelength will be:

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Answer: (b)

$\lambda \propto \dfrac{1}{\sqrt{E}}$ .
$E' = \dfrac{E}{4} \Rightarrow \lambda' = \lambda\sqrt{4} = 2\lambda$ .
So the answer is (b) $2\lambda$ .

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