the binding energy of a nucleus is 240.0 MeV. What is the mass defect of the nucleus in atomic mass units?
massdeficit=energy/speedlight
convert MeV to joules first.
To calculate the mass defect of a nucleus, you need to know the binding energy and use Einstein's mass-energy equivalence formula, E = mc^2.
1. Convert the binding energy from MeV to joules (J). 1 MeV is equal to 1.6 x 10^-13 joules.
- 240.0 MeV = 240.0 x 1.6 x 10^-13 J = 3.84 x 10^-11 J
2. Rearrange Einstein's formula to solve for mass (m):
- E = mc^2
- m = E / c^2, where c is the speed of light (3 x 10^8 m/s)
3. Find the mass defect in kilograms (kg) using the calculated binding energy and speed of light:
- m = (3.84 x 10^-11 J) / (3 x 10^8 m/s)^2 = 4.2667 x 10^-26 kg
4. Convert the mass defect from kilograms to atomic mass units (u). The atomic mass unit is defined as 1/12th the mass of a carbon-12 atom, which is approximately 1.66 x 10^-27 kg.
- Mass defect (u) = (4.2667 x 10^-26 kg) / (1.66 x 10^-27 kg/u) ≈ 25.7 u
Therefore, the mass defect of the nucleus is approximately 25.7 atomic mass units.