Question

Calculate the binding energy in MeV per nucleon of the nucleus of the isotope sulphur34. Would sulphur-34 fuse or undergo fission to tend towards stability?

a. Proton mass: 1.007276 a.m.u
b. Neutron mass: 1.008665 a.m.u
c. Sulphur-34 mass: 33.9678668 a.m.u

Answer 1

The binding energy of the nucleus of the isotope sulfur-34 is approximately 8.5 MeV per nucleon. Sulfur-34 would tend towards stability through fusion rather than fission.

Step-by-step explanation:

The binding energy per nucleon (BE/A) of a nucleus can be calculated using the formula:

BE/A = (Zm_p + Nm_n - M)/A

Where:

Z is the number of protons

N is the number of neutrons

m_p is the mass of a proton

m_n is the mass of a neutron

M is the mass of the nucleus

A is the mass number

For sulfur-34, Z = 16, N = 18, m_p = 1.007276 a.m.u, m_n = 1.008665 a.m.u, and M = 33.9678668 a.m.u. Plugging these values into the formula gives us:

BE/A = (161.007276 + 181.008665 - 33.9678668)/34 ≈ 8.5 MeV

This indicates that sulfur-34 has a binding energy of approximately 8.5 MeV per nucleon.

Sulfur-34 would tend towards stability through fusion rather than fission because fusion reactions release energy when light nuclei combine to form a heavier nucleus, and in this case, the resulting nucleus would have a higher binding energy per nucleon, making it more stable.