PYQ NEET- Dual Nature Of Matter And Radiation L-10

Question: 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#

A) 25

B) 75

C) 60

D) 50

Answer: 75#

Solution:#

de-Broglie wavelength of particle, $$ \begin{aligned} & \lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m E}} \ & \therefore \frac{\lambda^{\prime}}{\lambda}=\sqrt{\frac{E}{E^{\prime}}} \ & \Rightarrow \lambda^{\prime}=\frac{\lambda}{4} \end{aligned} $$

So, $%$ change in the de Broglie wavelength $$ =\frac{\lambda-\frac{\lambda}{4}}{\lambda} \times 100=75 % $$