Neutrons have a rest mass of 1.6749*10-27 kg (equivalent to 939.6 MeV).
If a certain neutron has a total energy of 949 MeV, what are its relativistic mass energy in MeV, its speed in m/s, its kinetic energy in MeV, and its momentum in kg.m.s-1?
To calculate the relativistic mass energy, speed, kinetic energy, and momentum of a neutron with a total energy of 949 MeV, we can use the equation for relativistic energy:
E = mc^2 / sqrt(1 - v^2/c^2)
Where:
E = total energy
m = relativistic mass energy
c = speed of light in a vacuum
v = velocity of the object
Step 1: Calculate relativistic mass energy (m):
We know the rest mass of the neutron (1.6749*10^-27 kg) is equivalent to 939.6 MeV. We can use the equation:
m = E / c^2
m = 939.6 MeV / (3 * 10^8 m/s)^2
m = 939.6 MeV / 9 * 10^16 m^2/s^2
m ≈ 1.049 * 10^-3 MeV
Step 2: Calculate speed (v):
Rearranging the relativistic energy equation, we get:
v = sqrt[(1 - (mc^2 / E)^2) * c^2]
v = sqrt[(1 - (1.049 * 10^-3 MeV)^2 / 949 MeV)^2 * (3 * 10^8 m/s)^2]
v ≈ 2.418 * 10^8 m/s
Step 3: Calculate kinetic energy:
The kinetic energy can be calculated using the equation:
Kinetic Energy (K.E.) = total energy (E) - rest mass energy (mc^2)
K.E. ≈ 949 MeV - 1.049 * 10^-3 MeV
K.E. ≈ 948.999 MeV
Step 4: Calculate momentum (p):
The momentum of the neutron can be calculated using the equation:
p = m * v
p = (1.049 * 10^-3 MeV) * (2.418 * 10^8 m/s)
p ≈ 2.535 * 10^-4 MeV.m/s
So, the relativistic mass energy of the neutron is approximately 1.049 * 10^-3 MeV, its speed is approximately 2.418 * 10^8 m/s, its kinetic energy is approximately 948.999 MeV, and its momentum is approximately 2.535 * 10^-4 MeV.m/s.