Question

Photons and alpha particles have the same de-Broglie wavelength. What is the same for both of them?

• A. Energy
• B. Time period
• C. Frequency
• D. Momentum

Hint:

Equal de-Broglie wavelengths imply equal momentum, regardless of the particle type.

Answer 1

The Correct Option is D

The de-Broglie wavelength is given by the relation: \[ \lambda = \frac{h}{p} \] where \( h \) is Planck's constant and \( p \) is the momentum of the particle.
If two particles — in this case, a photon and an alpha particle — have the same de-Broglie wavelength, then their momenta must be equal because: \[ \lambda = \frac{h}{p} \Rightarrow p = \frac{h}{\lambda} \] Hence, both must have the same momentum.
However, since their masses and natures are different, their energy and frequency will not be the same.