Question

What is the energy of a photon whose momentum is the same as that of the proton whose kinetic energy is 10 MeV? [The rest mass of the proton is 940 MeV/C)

Answer 1

To determine the energy of a photon with the same momentum as a 10 MeV kinetic energy proton, we must calculate the proton's momentum using relativistic mechanics and then use the photon's momentum-energy relationship to find the photon's energy.

Step-by-step explanation:

The task is to find the energy of a photon with the same momentum as a proton that has a kinetic energy of 10 MeV. To find this, we must first calculate the momentum of the proton using relativistic equations and then use this momentum to determine the photon's energy.

The kinetic energy (K) of the proton is given, K = 10 MeV. Since a proton's rest energy (E0) is given as 940 MeV (its mass m times c2), its total energy (E) can be calculated using E = E0 + K. The total energy and momentum (p) are related through E2 = p2c2 + m2c4, which allows us to solve for the proton's momentum. Once we have the momentum of the proton, we can use the relationship between photon momentum and energy, p = E/c, to find the photon's energy, because for a photon, m=0 and E2 = p2c2.

It is important to note that this approach is based on relativistic mechanics, which must be used because the kinetic energy of the proton is a significant fraction of its rest energy.

Answer 2

To find the energy of a photon with the same momentum as a proton with 10 MeV kinetic energy, we use the relativistic energy-momentum relationship to calculate the proton's momentum and then apply this to the photon's energy-momentum relationship.

Step-by-step explanation:

The question asked is: What is the energy of a photon whose momentum is the same as that of a proton whose kinetic energy is 10 MeV, given the rest mass of the proton is 940 MeV/c²? To solve this problem, we first determine the momentum of the proton using its kinetic energy and then use this momentum to find the energy of the corresponding photon.

The momentum p of the proton can be found using the relativistic energy-momentum relation:

E² = (pc)² + (m_0c²)²

where E is the total energy of the proton, m_0 is the rest mass of the proton, and c is the speed of light. Since the kinetic energy (K.E.) is 10 MeV and the rest energy of the proton (m_0c²) is 940 MeV, the total energy E is 950 MeV. By rearranging for momentum p, we can then compute the energy of the corresponding photon using the formula E = pc for a photon, because a photon's rest mass is zero.

The energy of the photon is then assumed to be equal to this momentum multiplied by the speed of light, c, in accordance with the photon's energy-momentum relationship.