Question

If kinetic energy of a proton is increased nine times , the wavelength of the de-Broglie wave associated with it would become?

Answer 1

Kinetic energy of proton = $\frac{p^2}{2m}$

If kinetic energy is increased to 9 times, momentum (p) is increased by 3 times.

So, De Broglie wavelength = $\frac{h}{p}$ is decreased by 3 times, i.e., from $\lambda$ to $\frac{\lambda }{3}$.