Dual Nature of Radiation and Matter - Result Question 8
8. 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 :
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======= ####8. 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 :
c3eec34ec6b1fad69db54a20ad4b2dca40c2aa54 (a) 25
(b) 75
(c) 60
(d) 50
[2014]
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Answer:
Correct Answer: 8. (b)
Solution:
(b) As we know
$\lambda=\frac{h}{P}=\frac{h}{\sqrt{2 mK}} \quad(\because P=\sqrt{2 mKE})$ or $\frac{\lambda_1}{\lambda_2}=\sqrt{\frac{K_2}{K_1}}=\sqrt{\frac{16 K}{K}}=\frac{4}{1}$
Therefore the percentage change in de-Broglie
wavelength $=\frac{1-4}{4} \times 100=-75 %$
