How to Calculate the Mass of One Atom of Uranium

Uranium fuels nuclear power plants.

Uranium contains the heaviest natural atoms, but these atoms don't all weigh the same. The element exists as multiple isotopes which vary in the number of neutrons in their nuclei. This variation leads to the isotopes' varied decay paths. All uranium atoms do, however, have the same number of electrons and protons. Physicists measure the mass of uranium atoms, and all atoms, in terms of unified atomic mass units (u). Optionally, you can convert this value to the more conventional unit of mass, such as grams.

Instructions

1. Multiply 92, which is the number of electrons in the atom, by 0.0005486, which is an electron's mass in u: 92 --- 0.0005486 u = 0.0504712 u.

2. Multiply 92, which is the number of protons in the atom, by 1.007276, which is the mass of a proton in u: 92 --- 1.007276 u = 92.669392 u.

3. Multiply the number of neutrons in the atom by 1.008665, which is the mass of a neutron in u. The number of neutrons is equal to the isotope's number (for example, 238 for uranium-238) minus its atomic number (92, the same as the number of protons or electrons in uranium). If you are calculating the mass of uranium-238, you would calculate that it has 146 neutrons (238 - 92 = 146), which have a mass of 146 --- 1.008665 u = 147.26509 u.

4. Add together the answers: 0.0504712 u + 92.669392 u + 147.26509 u = 239.984953 u.

5. To convert this answer to grams, multiply by 1.660538782 --- 10^-24: 239.984953 --- (1.660538782 --- 10^-27) = approximately 3.985 --- 10^-25 g.

References

• Purdue University: The Atom and Electromagnetic Radiation
• National Institute of Standards and Technology: Atomic Reference Data for Electronic Structure Calculations

Resources

• Lawrence Berkeley National Laboratory: ABC's of Nuclear Science
• University of Colorado: Atomic Mass Units