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If the kinetic energy of the particle is increased to 16 times its previous value

If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-broglie wavelength of the particle is

Options

(a) 25
(b) 75
(c) 60
(d) 50

Correct Answer:

75

Explanation:

For de-Broglie wavelength, λ₁ = h / p = h / √(2mK) —–(i)
λ₂ = h / √(2m 16K) = h / 4√(2mK) = λ₁ / 4 ——-(ii)
λ₂ = 25% of λ₁
There is 75% change in the wavelength.

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