Question

A nucleus of stable phosphorus has $15$ protons and $16$ neutrons. The difference of its atomic number and mass number is:
(A) $11$
(B) $12$
(C) $14$
(D) $16$

Answer 1

Hint
The atomic number is always equal to the number of protons present in the atom and the mass number is equal to the sum of proton and neutron present in the atom. After that we can see the difference between atomic number and mass number which is the required result.

Complete step by step solution
Atomic number in chemistry and physics, the atomic number of an element (also known as its proton number) is the number of protons found in the nucleus of an atom of that element, and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol $Z$.
As it is given that the number of protons is $15$.
Therefore, atomic number is $Z = 15$
Atomic mass or atomic weight is the average mass of atoms of an element, calculated using the relative abundance of isotopes in a naturally-occurring element. Atomic mass indicates the size of an atom.
As it is given that-
Number of neutrons $N = 16$
Number of protons $P = 15$
Mass number of element is $A = P + N$
$\Rightarrow A = 15 + 16 = 31$
Therefore, atomic number and mass number of phosphorus are $15$ and $31$ respectively.
Difference between atomic and mass number is $D = A - Z$
$\Rightarrow D = 31 - 15 = 16$
Hence, option (D) is correct.

Note
The number of electrons in a neutral atom is equal to the number of protons. The mass number of the atom (A) is equal to the sum of the number of protons and neutrons in the nucleus. The number of neutrons is equal to the difference between the mass number of the atom (A) and the atomic number (Z).