What is the relation between a photon's energy E and its momentum p?

What is the relation between a photon's energy E and its momentum p?

• A. p = E/c
• B. p = E c
• C. p = E c^2
• D. p = c/E

Answer: (A)

Photons have energy and momentum tied by E = p c. Since a photon has zero rest mass and travels at the speed of light, the relativistic energy-momentum relation reduces to E = p c, which rearranges to p = E/c. This also aligns with the wave-particle picture where E = h f and p = h/λ, with c = f λ, giving E = p c. The other forms don’t fit the units or the relationship: p = E c would mix energy with momentum in a way that doesn’t match how momentum scales; p = E c^2 is even more inconsistent with the established energy–momentum link; p = c/E inverts the ratio and fails to preserve the correct dependence on energy.

Photons have energy and momentum tied by E = p c. Since a photon has zero rest mass and travels at the speed of light, the relativistic energy-momentum relation reduces to E = p c, which rearranges to p = E/c. This also aligns with the wave-particle picture where E = h f and p = h/λ, with c = f λ, giving E = p c.

The other forms don’t fit the units or the relationship: p = E c would mix energy with momentum in a way that doesn’t match how momentum scales; p = E c^2 is even more inconsistent with the established energy–momentum link; p = c/E inverts the ratio and fails to preserve the correct dependence on energy.