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Chapter 26: Problem 67

A neutron, with rest energy 939.6 MeV, has momentum 935 MeV/c downward. What is its total energy?

Short Answer

Expert verified
Answer: The total energy of the neutron is approximately 1325.4 MeV.

Step by step solution

01

Write down the relativistic energy-momentum relation

The relativistic energy-momentum relation is given by the following formula: E^2 = (mc^2)^2 + (pc)^2 Here, E represents the total energy of the neutron, m is its rest mass, c is the speed of light, and p is its momentum.
02

Convert rest energy to rest mass

We are given the rest energy of the neutron, which is 939.6 MeV. Let's convert it to rest mass using the formula: m = E_rest / c^2 We are working in natural units, where c = 1. So the rest mass of the neutron is: m = 939.6 MeV/c^2
03

Plug values into the energy-momentum relation

Now, we will plug the known values into the energy-momentum relation formula. We have m = 939.6 MeV/c^2 and p = 935 MeV/c: E^2 = (939.6)^2 + (935)^2
04

Solve for total energy

Now, solve for E by taking the square root of both sides of the equation: E = sqrt((939.6)^2 + (935)^2) Calculate the value of E: E ≈ 1325.4 MeV
05

Interpret the result

The total energy of the neutron, which includes both its rest energy and kinetic energy, is approximately 1325.4 MeV.

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