Question

The binding energy per nucleon is maximum in the case of

• A. $\frac{4}{5}\mathrm{He}$
• B. $\frac{26}{26}\mathrm{Fe}^{56}$
• C. $\frac{56}{56}\mathrm{Ba}^{141}$
• D. $\frac{92}{92}\mathrm{U}^{225}$

Hint:

The peak of the binding energy per nucleon curve is around iron (A $\approx$ 56).

Answer 1

The Correct Option is B

The question asks which nucleus has the maximum binding energy per nucleon. To answer this, we need to understand what binding energy per nucleon means.

Binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. The binding energy per nucleon is a measure of the stability of a nucleus: the greater the binding energy per nucleon, the more stable the nucleus.

Typically, the binding energy per nucleon is highest for medium-sized nuclei. This is because, for light nuclei, adding more nucleons increases the binding energy, as the additional nucleons are generally within the attractive nuclear force range. However, for very heavy nuclei, the nuclear force is not sufficient to counteract the increasing repulsive electromagnetic forces due to the large number of protons.

Among the given options, let's discuss each one:

• \(\frac{4}{5}\mathrm{He}\): Helium-4 is a light nucleus with relatively low binding energy per nucleon compared to iron.
• \(\frac{26}{26}\mathrm{Fe}^{56}\): Iron-56 is known to have one of the highest binding energies per nucleon among all elements in the periodic table.
• \(\frac{56}{56}\mathrm{Ba}^{141}\): This is likely a typographical error, as Barium-141 does not have a binding energy per nucleon comparable to that of Iron-56.
• \(\frac{92}{92}\mathrm{U}^{225}\): Uranium-235 has a lower binding energy per nucleon because it is a very heavy nucleus, where the repulsion due to electromagnetic forces outweighs the attractive nuclear force.

Based on this analysis, the correct answer is \(\frac{26}{26}\mathrm{Fe}^{56}\), as Iron-56 is known to have the highest binding energy per nucleon, making it extremely stable.