What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from 1 nm to 0.5 nm? (a) Four times its initial energy. (b) Five times its initial energy. (c) Two times its initial energy. (d) Three times its initial energy.

Answer: (d). K ∝ (1)/(λ²). λ halves ( 1 nm → 0.5 nm) ⇒ K' = 4K. Additional energy = 4K - K = 3K. So the answer is (d) three times its initial energy.

What is the additional energy that should be supplied to a moving… | MHT CET 2021 (20 Sep, Shift 2)

Q98MHT CET 2021 · 20 SEP · SHIFT 2Medium

Matter Waves: de Broglie Wavelength

What is the additional energy that should be supplied to a moving electron to reduce its de Broglie wavelength from $1\text{ nm}$ to $0.5\text{ nm}$ ?

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Answer: (d)

$K \propto \dfrac{1}{\lambda^2}$ .
$\lambda$ halves ( $1\text{ nm} \to 0.5\text{ nm}$ ) $\Rightarrow K' = 4K$ .
Additional energy $= 4K - K = 3K$ .
So the answer is (d) three times its initial energy.

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