The formula to calculate the Mass Deficiency is:
\[ \Delta m = (N_p \cdot m_p) + (N_n \cdot m_n) - m_{nucleus} \]
Where:
Mass deficiency, also known as mass defect, refers to the difference between the mass of an atomic nucleus and the sum of the masses of its constituent protons and neutrons. This difference arises because a portion of the mass is converted into binding energy that holds the nucleus together, according to Einstein’s mass-energy equivalence principle (E=mc²). The mass deficiency is a measure of the stability of the nucleus; the greater the mass defect, the more stable the nucleus.
Let's say you have 2 protons with a mass of 1.00728 u each, 2 neutrons with a mass of 1.00866 u each, and a nucleus mass of 4.00150 u. Using the formula:
\[ \Delta m = (2 \cdot 1.00728) + (2 \cdot 1.00866) - 4.00150 = 0.02938 \, \text{u} \]
So, the mass deficiency (Δm) would be 0.02938 u.