$(a)$ How many neutrons are present in $C-14$ isotope of carbon?
$(b)$ How many protons does $He^{2+}$ ion possess?
$(c)$ How many maximum electrons can be filled in the $3^{rd}$ orbit of an atom?
$(d)$ How many electrons does $He^{2+}$ ion possess?

(N/A) The mass number of $C-14$ is $14$ and the atomic number is $6$. The number of neutrons is calculated as $\text{Mass number} - \text{Atomic number} = 14 - 6 = 8$ neutrons.
$(b)$ The atomic number of Helium $(He)$ is $2$,which represents the number of protons. The $He^{2+}$ ion is formed by the loss of electrons,but the number of protons remains unchanged. Thus,it has $2$ protons.
$(c)$ The maximum number of electrons in an orbit is given by the formula $2n^2$,where $n$ is the orbit number. For the $3^{rd}$ orbit,$n = 3$. Therefore,$2(3)^2 = 2 \times 9 = 18$ electrons.
$(d)$ $A$ neutral Helium atom has $2$ electrons. The $He^{2+}$ ion is formed by losing $2$ electrons. Therefore,$2 - 2 = 0$ electrons.