The electron-volt, eV, is a unit of energy (1eV = 1.602 ·10–19 J, 1 MeV = 1.602 ·10–13 J). Since the unit of momentum is an energy unit divided by a velocity unit, nuclear physicists usually specify momenta of nuclei in units of MeV/c, where c is the speed of light (c = 2.998 ·108 m/s). In the same units, the mass of a proton (1.673 ·10–27 kg) is given as 938.3 MeV/c2. If a proton moves with a speed of 7500 km/s, what is its momentum in units of MeV/c?
m = 938.3 MeV/c^2
v = 7500 km/s
m v = 938.3 MeV/c^2 7500 km/s =
938.3 MeV/c (7500 km/s)/c =
23.47 MeV/c
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To find the momentum of a proton moving at a speed of 7500 km/s in units of MeV/c, we need to convert the given speed to units of meters per second (m/s) and then calculate the momentum using the formula:
Momentum = (Mass * Velocity) / Speed of Light
Let's begin by converting the given speed from km/s to m/s. We know that 1 km = 1000 m, so:
Speed in m/s = 7500 km/s * (1000 m/1 km) = 7.5 * 10^6 m/s
Now we can plug the values into the momentum formula:
Momentum = (Mass * Velocity) / Speed of Light
= (938.3 MeV/c^2 * (7.5 * 10^6 m/s)) / (2.998 * 10^8 m/s)
Next, let's convert the mass of the proton from MeV/c^2 to kg. We know that 1 MeV = 1.602 * 10^-19 J, and since 1 J = 1 kg*m^2/s^2, we can convert it accordingly:
Mass in kg = 938.3 MeV/c^2 * (1.602 * 10^-19 J/1 MeV) * (1 kg*m^2/s^2 / (3*10^8 m/s)^2)
Simplifying this expression, we get:
Mass in kg = 938.3 * (1.602 * 10^-19) * (1 / (3*10^8)^2)
Now, we can substitute this value into the momentum formula:
Momentum = (Mass * Velocity) / Speed of Light
= (938.3 * (1.602 * 10^-19) * (1 / (3*10^8)^2) * (7.5 * 10^6)) / (2.998 * 10^8)
Calculating this expression will give us the momentum of the proton in units of MeV/c.