Calculate the number of particles in each of the following:
$(a)$ $48 \,g$ of $Mg$
$(b)$ $8 \,g$ of $O_2$
$(c)$ $0.1$ mole of carbon (Atomic mass $Mg = 24 \,u, O = 16 \,u, C = 12 \,u$,Avogadro constant $= 6.022 \times 10^{23}$)

(N/A) The number of atoms $= \frac{\text{Given mass}}{\text{Molar mass}} \times \text{Avogadro constant}$
$\Rightarrow N = \frac{m}{M} \times N_A = \frac{48}{24} \times 6.022 \times 10^{23} = 2 \times 6.022 \times 10^{23} = 12.044 \times 10^{23} \text{ atoms}$.
$(b)$ The number of molecules $= \frac{\text{Given mass}}{\text{Molar mass}} \times \text{Avogadro constant}$
$\Rightarrow N = \frac{8}{32} \times 6.022 \times 10^{23} = 0.25 \times 6.022 \times 10^{23} = 1.5055 \times 10^{23} \text{ molecules}$.
$(c)$ The number of particles (atoms) $= \text{Number of moles} \times \text{Avogadro constant}$
$\Rightarrow N = 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \text{ atoms}$.