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 calculated using the formula: \[ \lambda = \frac{h}{p}, \] where $h$ represents Planck's constant and $p$ denotes the momentum of the particle. When two particles exhibit identical de Broglie wavelengths, their momenta must be equal. This is due to the inverse relationship between $\lambda$ and $p$. Consequently, while their momenta are the same, their masses, and therefore their speeds and energies, may vary. For an electron and a proton in motion, if they possess the same wavelength, it follows that: \[ p_{\text{electron}} = p_{\text{proton}}. \] Therefore, the common characteristic is their: \[ \boxed{\text{momentum}}. \]