An atomic mass unit, or amu, is one-twelfth of the mass of an unbound atom of carbon-12, and it used to express the mass of atomic and subatomic particles. The joule is the unit of energy in the International System of Units. Understanding of the relationship between the binding energy and the mass defect in Albert Einstein's Theory of Relativity equation clarifies the process of converting amu into joules. In the equation the mass defect is the “vanishing” mass of the protons and neutrons that is converted to energy that holds the nucleus together.

### Conversion 1 amu into joule

Remember that the mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons that compose it. In calculating the mass defect use the full accuracy of mass measurements, because the difference in mass is small compared to the mass of the atom. Rounding off the masses of atoms and particles to three or four significant digits prior to the calculation will result in a calculated mass defect of zero.

Convert the atomic mass unit (amu) into kilograms. Remember that 1 amu = 1.66053886*10^-27 kg.

Write down Einstein's formula for the binding energy \"?E\": ?E = ?m_c^2, where \"c\" is the velocity of light that is equal to 2.9979_10^8 m/s; \"?m\" is the mass defect and equals 1 amu in this explanation.

Substitute the value of 1 amu in kilograms and the value of the velocity of light in Einstein's equation. ?E= 1.66053886_10^-27 kg_(2.9979*10^8 m/s) ^2.

Use your calculator to find ?E by following the formula in Step 4.

This will be your answer in kg_m^2 /s^2: ?E= 1.66053886_10^-27 _8.9874_10^16=1.492393*10^-10.

Convert 1.4923933_10^-10 kg_m^2 /s^2 to joules \"J\" Knowing that 1 kg_m^2 /s^2 = 1 J, the answer will be 1 amu = 1.4923933_10^-10 J.

### Calculation example

Convert the mass defect (amu) of lithium-7 into joules \"J\". The nuclear mass of lithium-7 equals 7.014353 amu. The lithium nucleon number is 7 (three protons and four neutrons).

Look up the masses of protons and neutrons (the mass of a proton is 1.007276 amu, the mass of neutron is 1.008665 amu) adding them together to get the total mass: (3_1.007276) + (4_1.008665). The result is 7.056488 amu. Now, to find the mass defect, subtract the nuclear mass from the total mass: 7.056488 - 7.014353 = 0.042135 amu.

Convert amu into kilograms (1 amu = 1.6606_10^-27 kg) multiplying 0.042135 by 1.6606_10^-27. Result will be 0.0699693_10^-27 kg. Using Einstein's formula of mass-energy equivalence (?E = ?m_c^2) substitute the values of mass defect in kilograms and the value of the velocity of light \"c\" in meters-per-second to find energy \"E\". E = 0.0699693_10^-27_(2.9979_10^8)^2 = 6.28842395_ 10^-12 kg*m^2/s^2. This will be your answer in joules \"J\".