Question

The ${m_p}$ and ${m_n}$ are masses of proton and neutron respectively. An element of mass $M$ has $Z$ protons and $N$ neutrons then:
A. $M > Z{m_p} + N{m_n}$
B. $M = Z{m_p} + N{m_n}$
C. $M < Z{m_p} + N{m_n}$
D. $M$ may be greater than less than or equal to $Z{m_p} + N{m_n}$, depending on nature of element

Answer 1

Write down the given information first. Then write down the expression for the actual atomic mass of the element. Recall the relation between actual atomic mass and mass of the element. Observe which of the given options match with the relation obtained.

Complete step by step answer:
Given, mass of proton, ${m_p}$,mass of neutron, ${m_n}$,mass of the element, $M$,number of protons, $Z$ and number of neutrons, $N$.The actual atomic mass of the element is total mass of proton plus total mass of neutron that is,
${M_{actual}} = Z{m_p} + N{m_n}$
The mass of an element is always slightly less than the actual atomic mass of the element that is,
$M < Z{m_p} + N{m_n}$
Therefore, observing the options we see that it matches with option (C)

Hence, the correct answer is option C.

Note: The difference between the actual atomic mass and mass of an element is known as mass defect. This mass defect can represent the energy released when the nucleus was formed. This energy is also known as nuclear binding energy. There are few points that one should always remember, neutrons and protons are collectively known as nucleons. These nucleons are bound to each other by strong nuclear force. There are four types of forces in nature, gravitational, electromagnetic, weak and strong force. Among these forces strong force is the strongest force and gravitational force is the weakest.