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 de Broglie relation connects a particle's or wave's wavelength \( \lambda \) to its linear momentum \( p \): \[ \lambda = \frac{h}{p} \Rightarrow p = \frac{h}{\lambda} \] Therefore, if two entities, such as a photon and an electron, share the same wavelength \( \lambda \), they must also have the same linear momentum \( p \). This equality in momentum does not, however, imply equality in:- Energy: Energy is dependent on mass and velocity for particles, and on frequency for photons.- Velocity: Photons consistently travel at the speed of light, unlike electrons.- Angular momentum: Angular momentum is not necessarily the same, as it is contingent upon geometry and motion.