Answer :
The binding energy per nucleon for Ba-141 is approximately -8.33 MeV/nucleon.
Here's how we can calculate it:
1. **Mass defect:**
- Calculate the mass defect, which is the difference between the actual mass of the nucleus and the sum of the individual masses of its protons and neutrons.
- Mass defect of Ba-141 = 140.883 amu - (56 * 1.007276 amu + 85 * 1.008665 amu) ≈ 0.10873 amu
2. **Conversion to energy:**
- Convert the mass defect to energy using Einstein's mass-energy equivalence: E = mc².
- Energy equivalent = mass defect * speed of light^2 * conversion factor
- Energy equivalent = 0.10873 amu * (299792458 m/s)² * (1.60217662 x 10⁻¹³ J/amu) ≈ 1.6515 x 10⁻¹¹ J
3. **Binding energy per nucleon:**
- Divide the total binding energy by the number of nucleons in the nucleus (56 protons + 85 neutrons = 141 nucleons).
- Binding energy per nucleon = total binding energy / number of nucleons
- Binding energy per nucleon = (1.6515 x 10⁻¹¹ J) / 141 nucleons ≈ -8.33 MeV/nucleon (negative sign indicates energy is released during binding)
Therefore, the binding energy per nucleon for Ba-141 is approximately -8.33 MeV/nucleon. This value indicates that a significant amount of energy is released when individual nucleons are combined to form the Ba-141 nucleus.
