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$M_n$ and $M_p$ represent the mass of neutron and proton respectively. An element having mass M has N neutrons and Z protons, then the correct relation will be : -
A
$M \lt \{N \cdot M_n + Z \cdot M_p\}$
B
$M \gt \{N \cdot M_n + Z \cdot M_p\}$
C
$M = \{N \cdot M_n + Z \cdot M_p\}$
D
$M = N\{M_n + M_p\}$
Detailed Solution
When nucleons combine to form a nucleus, energy (the binding energy) is released. By $E = \Delta mc^2$, this corresponds to a loss of mass.
So the mass of a nucleus is always less than the sum of the masses of its free protons and neutrons. The difference is the mass defect: $\Delta m = (NM_n + ZM_p) - M$.
So $M \lt \{N \cdot M_n + Z \cdot M_p\}$.
So the mass of a nucleus is always less than the sum of the masses of its free protons and neutrons. The difference is the mass defect: $\Delta m = (NM_n + ZM_p) - M$.
So $M \lt \{N \cdot M_n + Z \cdot M_p\}$.