What is the rest mass energy equivalent in MeV of 1 atomic mass unit as calculated directly from E=mc2?
The Correct Answer and Explanation is:
The rest mass energy equivalent of 1 atomic mass unit (amu) can be calculated directly from Einstein’s famous equation, E=mc2E = mc^2E=mc2, where:
- EEE is the energy,
- mmm is the mass,
- ccc is the speed of light in a vacuum, approximately 3.00×108 m/s3.00 \times 10^8 \, \text{m/s}3.00×108m/s.
Step 1: Conversion of atomic mass unit to kilograms
First, we need to express the mass in kilograms. The atomic mass unit is defined as: 1 amu=1.66053906660×10−27 kg1 \, \text{amu} = 1.66053906660 \times 10^{-27} \, \text{kg}1amu=1.66053906660×10−27kg
Step 2: Calculation of energy
Next, substitute this mass into the equation E=mc2E = mc^2E=mc2. We have: E=(1.66053906660×10−27 kg)×(3.00×108 m/s)2E = (1.66053906660 \times 10^{-27} \, \text{kg}) \times (3.00 \times 10^8 \, \text{m/s})^2E=(1.66053906660×10−27kg)×(3.00×108m/s)2
First, calculate c2c^2c2: c2=(3.00×108)2=9.00×1016 m2/s2c^2 = (3.00 \times 10^8)^2 = 9.00 \times 10^{16} \, \text{m}^2/\text{s}^2c2=(3.00×108)2=9.00×1016m2/s2
Now calculate the energy: E=(1.66053906660×10−27)×(9.00×1016)=1.49448515994×10−10 JE = (1.66053906660 \times 10^{-27}) \times (9.00 \times 10^{16}) = 1.49448515994 \times 10^{-10} \, \text{J}E=(1.66053906660×10−27)×(9.00×1016)=1.49448515994×10−10J
Step 3: Conversion from joules to electron volts
Since the energy is typically expressed in electron volts (eV) in atomic and nuclear physics, we need to convert joules to eV. The conversion factor is: 1 eV=1.60218×10−19 J1 \, \text{eV} = 1.60218 \times 10^{-19} \, \text{J}1eV=1.60218×10−19J
Thus, the energy in eV is: E=1.49448515994×10−10 J1.60218×10−19 J/eV=931.494 MeVE = \frac{1.49448515994 \times 10^{-10} \, \text{J}}{1.60218 \times 10^{-19} \, \text{J/eV}} = 931.494 \, \text{MeV}E=1.60218×10−19J/eV1.49448515994×10−10J=931.494MeV
Final Answer:
The rest mass energy equivalent of 1 atomic mass unit (1 amu) is approximately 931.5 MeV.
This value is significant because it is the energy released when an atomic mass unit of matter is completely converted into energy, as per Einstein’s theory of relativity. This rest mass energy is a key concept in nuclear physics and is central to understanding the energy produced in nuclear reactions, such as those in the sun and nuclear power plants.
