Question

The waves associated with a moving electron and a moving proton have the same wavelength $\lambda$. It implies that they have the same:

• A. momentum
• B. angular momentum
• C. speed
• D. energy

Hint:

The de Broglie wavelength $\lambda$ depends only on the momentum $p$ of the particle. If two particles have the same $\lambda$, they must have the same momentum, regardless of their masses or speeds.

Answer 1

The Correct Option is A

The de Broglie wavelength $\lambda$ of a particle is given by: \[ \lambda = \frac{h}{p}, \] where: \begin{itemize} \item $h$ is Planck's constant, \item $p$ is the momentum of the particle. \end{itemize} If two particles have the same de Broglie wavelength, then their momenta must be the same, because $\lambda$ is inversely proportional to $p$. However, their masses may differ, and thus their speeds and energies can be different. For a moving electron and a moving proton, having the same wavelength implies: \[ p_{\text{electron}} = p_{\text{proton}}. \] Thus, the correct answer is: \[ \boxed{\text{momentum}}. \]