sketch the variation of binding energy per nucleon with nucleon number

Mass defect and nuclear binding energy

🔬 Mass defect is the difference between the sum of the masses of the individual protons and neutrons and the actual mass of the nucleus. The missing mass has been converted into binding energy that holds the nucleus together.

💡 Binding energy per nucleon (the binding energy curve) tells us how tightly each nucleon is bound. It is calculated as:

$$\frac{E_b}{A} = \frac{(Z m_p + N m_n - M)c^2}{A}$$

Where Z = number of protons, N = number of neutrons, M = mass of the nucleus, and A = Z+N.

Analogy: Building a Lego Tower

Imagine you have a pile of Lego bricks (protons and neutrons). If you simply stack them, the tower would weigh the sum of all bricks. But when you glue the bricks together, the glued tower weighs a little less because some energy is released as glue. That “missing weight” is the mass defect, and the glue’s energy is the binding energy that keeps the tower standing.

Step‑by‑step: How to find the mass defect

1. Write down the number of protons Z and neutrons N for the nucleus.
2. Calculate the separated mass:

$$M_{\text{separated}} = Z\,m_p + N\,m_n$$

3. Measure or look up the actual nuclear mass M.
4. Find the mass defect:

$$\Delta m = M_{\text{separated}} - M$$

5. Convert to binding energy using c = 3.00×10⁸ m/s:

$$E_b = \Delta m\,c^2$$

6. Divide by the nucleon number A to get the binding energy per nucleon.

Binding energy per nucleon – the “curve”

The curve rises steeply from very light nuclei, reaches a maximum around iron (Fe‑56), and then slowly falls for heavier nuclei. This tells us:

• Light nuclei (A < 56) can release energy by fusion (joining together).
• Heavy nuclei (A > 56) can release energy by fission (splitting apart).

Sample data and a quick visual sketch

(The bar length is roughly proportional to the binding energy per nucleon.)

Exam tip: Remember the curve shape

When you see a question about energy release:

• For light nuclei (A < 56), think fusion.
• For heavy nuclei (A > 56), think fission.

Use the formula for binding energy per nucleon to compare two nuclei – the one with the higher value is more stable.

Quick check: Is this nucleus stable?

Calculate E_b/A for the two nuclei and compare. The one with the higher value is closer to the peak of the curve and is therefore more stable.