Question

Mn and Mp represet the mass of neutron and proton respectively. An element having mass M has N neutron and Z-protons, then the correct relation will be 

• A. M < {N.Mn + Z.Mp}M < {N.Mn + Z.Mp}
• B. M > {N.Mn + Z.Mp}
• C. M = {N.Mn+Z.Mp}
• D. M=N{Mn + Mp}

Answer 1

The Correct Option is A

To solve this problem, we need to understand the relationship between the mass of an atomic nucleus and its constituent particles: neutrons and protons.

An atomic nucleus is composed of protons and neutrons. The total mass of an element (denoted as M) with N neutrons and Z protons can be expressed as:

M = N \cdot M_n + Z \cdot M_p - \Delta E/c^2

Here, M_n and M_p are the masses of a neutron and a proton, respectively, and \Delta E/c^2 represents the binding energy per nucleon, converted into mass using Einstein's mass-energy equivalence. This binding energy accounts for the fact that assembled nuclei have less mass than the sum of their individual nucleons due to the energy released when they bind together (mass defect).

This is why the mass of the element M is slightly less than the sum of the masses of all its neutrons and protons. Therefore, we can write the inequality as:

M < N \cdot M_n + Z \cdot M_p

This corresponds to the correct answer:

• M < \{N \cdot M_n + Z \cdot M_p\}

Explanation: The key concept here is the mass defect due to the nuclear binding energy. When protons and neutrons combine to form a nucleus, a significant amount of energy is released in the form of binding energy, leading to a reduction in total mass compared to separate nucleons. This results in the actual atomic mass being less than the sum of the masses of its protons and neutrons.