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Chapter 5: Problem 61

If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and \(939.6 \mathrm{MeV}\) respectively, what is the difference in their mass in kilograms?

Short Answer

Expert verified
The difference in mass between a proton and a neutron is approximately \(2.29 \times 10^{-30}\) kilograms.

Step by step solution

01

Convert energy to mass

First, we need to find the mass of each particle using the given energy values and Einstein's equation: \(E = mc^2\) We can rearrange this equation to solve for mass: \(m = \frac{E}{c^2}\) The given rest energies: E_proton = 938.3 MeV E_neutron = 939.6 MeV We will first convert energies from MeV to Joules since the speed of light (c) is in m/s. 1 MeV = 1.60219x10^-13 Joules E_proton = (938.3 MeV) * (1.60219x10^-13 J/MeV) = 1.50326x10^-10 J E_neutron = (939.6 MeV) * (1.60219x10^-13 J/MeV) = 1.50517x10^-10 J Now, we need to use these energy values to find the mass, and we need the speed of light (c) for that: c = 3x10^8 m/s
02

Calculate the masses

Using the energy values in Joules, calculate the mass for each particle: m_proton = E_proton / c^2 = (1.50326x10^-10 J) / (3x10^8 m/s)^2 = 1.67264x10^-27 kg m_neutron = E_neutron / c^2 = (1.50517x10^-10 J) / (3x10^8 m/s)^2 = 1.67493x10^-27 kg
03

Find the difference in mass

Now that we have the mass of a proton and a neutron, we can find the difference in mass: mass_difference = m_neutron - m_proton = 1.67493x10^-27 kg - 1.67264x10^-27 kg = 2.29x10^-30 kg The difference in mass between a proton and a neutron is approximately 2.29x10^-30 kilograms.

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