14. Photon A has twice the energy of photon B. What is the ratio of the momentum of A to that of B
Question
- Photon A has twice the energy of photon B. What is the ratio of the momentum of A to that of B
Solution
The energy of a photon is given by the equation E = hf, where h is Planck's constant and f is the frequency of the photon. The momentum of a photon is given by the equation p = E/c, where c is the speed of light.
Step 1: Given that the energy of photon A is twice that of photon B, we can write this as EA = 2EB.
Step 2: Substituting the energy equation into this, we get hfA = 2hfB, where fA is the frequency of photon A and fB is the frequency of photon B.
Step 3: Simplifying this, we find that fA = 2fB. This means that the frequency of photon A is twice that of photon B.
Step 4: Now, substituting the frequency ratio into the momentum equation, we get pA = hfA/c = 2hfB/c = 2pB.
So, the ratio of the momentum of photon A to that of photon B is 2:1.
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