Question

The wavelength of a photon is equal to the wavelength associated with an electron. Both will have the same value of:

• A. energy
• B. angular momentum
• C. velocity
• D. linear momentum

Hint:

Equal wavelengths imply equal linear momentum, using \( p = \frac{h}{\lambda} \), regardless of whether the particle is massless (like a photon) or has mass (like an electron).

Answer 1

The Correct Option is D

The wavelength \( \lambda \) associated with any particle or wave is related to its linear momentum \( p \) using the de Broglie relation: \[ \lambda = \frac{h}{p} \Rightarrow p = \frac{h}{\lambda} \] Thus, if two entities (like a photon and an electron) have the same wavelength \( \lambda \), they must have the same linear momentum \( p \). However, this does not imply that they have the same: - Energy: because energy depends on mass and velocity for particles, and frequency for photons. - Velocity: photons always travel at the speed of light, whereas electrons do not. - Angular momentum: not necessarily the same, as it depends on geometry and motion.