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Q.

The de-Broglie wavelength of a particle of kinetic energy K is $λ$ . What will be the wavelength of the particle, if its kinetic energy is $\frac{K}{9} ?$

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a

$4 λ$

b

$λ$

c

$2 λ$

d

$3 λ$

answer is C.

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Detailed Solution

De-Broglie wavelength $λ = \frac{h}{\sqrt{2 mK}}$

$When the kinetic energy is \frac{K}{9}, then λ^{'} = \frac{h}{\sqrt{2 m (\frac{K}{9})} = \frac{3 h}{\sqrt{2 mK}}} = 3 λ$

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The de-Broglie wavelength of a particle of kinetic energy K is λ. What will be the wavelength of the particle, if its kinetic energy is K9?