A photon in light beam A has twice the energy of a photon in light beam B.The ratio p_A/p_B of their momenta is: A)1/2 B)1/4 C)1 D)2 E)4

Question

Quizplus · Accepted Answer

We know that the energy of a photon is directly proportional to its frequency (and inversely proportional to its wavelength). Therefore, since the energy of the photon in beam A is twice that of the photon in beam B, we can deduce that the frequency of the photon in beam A is twice that of the photon in beam B. Now, we use the fact that the energy of a photon is given by E=hf, where h is Planck's constant (a constant of nature). Since we know that the frequency of the photon in beam A is twice that of the photon in beam B, we can write: EA = 2EB hfA = 2hfB fA/fB = 2 Next, we use the fact that momentum p of a photon is given by p=E/c, where c is the speed of light (another constant of nature). So, the ratio of their momenta is: p_A/p_B = (EA/c)/(EB/c) = EA/EB = 2 Therefore, the correct answer is D) 2.

A Photon in Light Beam a Has Twice the Energy