Mass Defect Calculator
Free Mass defect Calculator for nuclear chemistry. Enter variables to compute results with formulas and detailed steps.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Mass Defect = (Z x mp + N x mn + Z x me) - M_atom
The mass defect is the difference between the sum of individual particle masses (protons, neutrons, electrons) and the measured atomic mass. Binding energy equals the mass defect times 931.494 MeV/amu.
Worked Examples
Example 1: Helium-4 Mass Defect
Problem:Calculate the mass defect and binding energy of He-4 (2 protons, 2 neutrons, atomic mass 4.002602 amu).
Solution:Protons: 2 x 1.007276 = 2.014552 amu\nNeutrons: 2 x 1.008665 = 2.017330 amu\nElectrons: 2 x 0.000549 = 0.001098 amu\nTotal = 4.032980 amu\nMass defect = 4.032980 - 4.002602 = 0.030378 amu\nBE = 0.030378 x 931.494 = 28.296 MeV
Result:Mass defect = 0.0304 amu, BE = 28.3 MeV, BE/A = 7.07 MeV
Example 2: Iron-56 Mass Defect
Problem:Calculate for Fe-56 (26 protons, 30 neutrons, atomic mass 55.934936 amu).
Solution:Protons: 26 x 1.007276 = 26.189176 amu\nNeutrons: 30 x 1.008665 = 30.259950 amu\nElectrons: 26 x 0.000549 = 0.014274 amu\nTotal = 56.463400 amu\nMass defect = 56.463400 - 55.934936 = 0.528464 amu\nBE = 492.26 MeV, BE/A = 8.79 MeV
Result:Mass defect = 0.5285 amu, BE = 492.3 MeV, BE/A = 8.79 MeV
Frequently Asked Questions
What is mass defect?
Mass defect is the difference between the total mass of individual protons, neutrons, and electrons that make up an atom and the actual measured mass of the atom. The actual atomic mass is always less than the sum of its parts because some mass is converted to energy that holds the nucleus together (binding energy). This relationship is described by Einstein equation E = mc^2. A larger mass defect means stronger nuclear binding and a more stable nucleus.
How does mass defect relate to E = mc^2?
Einstein mass-energy equivalence E = mc^2 directly explains mass defect. When nucleons combine to form a nucleus, the binding energy released causes a measurable decrease in mass. For example, a helium-4 nucleus has a mass defect of 0.030 amu, corresponding to 28.3 MeV of binding energy. This energy was released when the nucleus formed and would need to be supplied to break it apart. The conversion factor 1 amu = 931.494 MeV/c^2 is derived from E = mc^2.
What is the difference between mass and weight?
Mass measures the amount of matter in an object (kilograms) and is constant everywhere. Weight is the gravitational force on that mass (newtons) and varies by location. On Earth, a 1 kg object weighs about 9.8 newtons. In everyday use, the terms are often used interchangeably.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy