# Chemistry Calculation: Nuclear Binding Energy of Sulfur Atom

What is the nuclear binding energy of a 32/16 S atom with a measured atomic mass of 31.972 070 u?

The nuclear binding energy is the energy equivalent to the mass defect, which is the difference between the mass of a nucleus and the sum of the masses of its nucleons. To calculate the nuclear binding energy of a 32/16 S atom, we first determine the mass defect. Given: Atomic mass of 32/16 S = 31.972 070 u Total mass of nucleons = 32.255 20 u Mass defect = Total mass of nucleons - Mass of S-32 Mass defect = 32.255 20 u - 31.972 070 u Mass defect = 0.283 13 u Next, we convert the mass defect from unified atomic mass units to kilograms: Mass defect = 0.283 13 u x (1.66 10^-27 kg / 1 u) Mass defect = 4.700 x 10^-28 kg Now, we use Einstein's equation (E = mc^2) to convert the mass defect into energy: E = 4.700 x 10^-28 kg x (2.998 x 10^8 m/s)^2 E = 4.224 x 10^-11 J Therefore, the nuclear binding energy of a 32/16 S atom is 4.224 x 10^-11 Joules.

## Calculation Process:

**1. Determine Mass Defect:**The mass defect is calculated as the difference between the total mass of nucleons and the measured atomic mass of the Sulfur-32 atom.

**2. Convert to Kilograms:**The mass defect is then converted from unified atomic mass units to kilograms using the conversion factor provided.

**3. Calculate Nuclear Binding Energy:**Using Einstein's famous equation E = mc^2, we find the energy equivalent of the mass defect, which represents the nuclear binding energy of the Sulfur-32 atom. In conclusion, the nuclear binding energy of a 32/16 S atom is 4.224 x 10^-11 Joules. This energy corresponds to the mass difference between the nucleus and the sum of its nucleons, showcasing the powerful binding forces that hold the atom together.