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 [2014]

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Solution

Q.
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 [2014]

1 25

2 75

3 60

4 50

Ans.
(2)

de Broglie wavelength,

$λ = \frac{h}{\sqrt{2 m K}}$ ...(i)

where $m$ is the mass and $K$ is the kinetic energy of the particle. When kinetic energy of the particle is increased to 16 times, then its de Broglie wavelength becomes,

$λ' = \frac{h}{\sqrt{2 m (16 K)}} = \frac{1}{4} \frac{h}{\sqrt{2 m K}} = \frac{λ}{4} (Using (i))$

% change in the de Broglie wavelength

$= \frac{λ - λ'}{λ} \times 100 = (1 - \frac{λ'}{λ}) \times 100 = (1 - \frac{1}{4}) \times 100 = 75 %$

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