If the kinetic energy of an electron is quadrupled, its de Broglie wavelength is
A) quadrupled.
B) doubled.
C) halved.
D) quartered.

Question

Quizplus · Accepted Answer

The de Broglie wavelength $\lambda$ of a particle is given by $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is the momentum of the particle. For an electron, its kinetic energy $E_k$ is related to its momentum $p$ by the relation $E_k = \frac{p^2}{2m}$, where $m$ is the mass of the electron. If the kinetic energy is quadrupled, then the new kinetic energy is $4E_k = \frac{(2p)^2}{2m}$, implying that the momentum $p$ is doubled. Since the de Broglie wavelength is inversely proportional to the momentum ($\lambda \propto \frac{1}{p}$), if the momentum is doubled, the de Broglie wavelength is halved.

If the Kinetic Energy of an Electron Is Quadrupled, Its