Question: Which of the following electromagnetic waves has photons of largest momentum?
Correct Option: (A) X-rays
Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]
The momentum ($p$) of a photon is related to its wavelength ($\lambda$) by the de Broglie relation:
$$p = \frac{h}{\lambda}$$Where:
- $h$ is Planck's constant.
- $\lambda$ is the wavelength of the electromagnetic wave.
From the relation, it is evident that momentum is inversely proportional to wavelength ($p \propto \frac{1}{\lambda}$).
Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]
Comparing the wavelengths of the given electromagnetic spectrum regions:
- $\lambda_{\text{AM radio}} > \lambda_{\text{TV}} > \lambda_{\text{Microwaves}} > \lambda_{\text{X-rays}}$
Since X-rays have the shortest wavelength among the given options, we substitute this into the momentum relation:
$$p_{\text{X-ray}} = \frac{h}{\lambda_{\text{shortest}}} \implies p_{\text{max}}$$Step 3 (Final Concluded Answer): [0.25 Mark]
Because X-rays possess the smallest wavelength in the provided list, they must possess the highest momentum. Therefore, (A) X-rays is the correct answer.
💡 EL10 Concept Insight: Think of momentum like the "punch" of a photon; because X-rays have the shortest, most tightly packed waves, they carry the most energy and the biggest punch compared to long, lazy radio waves.