The composition of the nuclei of two atomic species $\mathrm{X}$ and $\mathrm{Y}$ are given as under $\mathrm{Protons}=6\left(\mathrm{X}\right):6\left(\mathrm{Y}\right)$, $\mathrm{Neutrons}=6\left(\mathrm{X}\right):8\left(\mathrm{Y}\right)$. Give the mass numbers of $\mathrm{X}$ and $\mathrm{Y}$. What is the relation between the two species?

Mass number:

• It is the sum of the number of protons and the number of neutrons present in the nuclei of an atom.
• $\mathrm{Mass}\mathrm{number}=\mathrm{Number}\mathrm{of}\mathrm{protons}+\mathrm{Number}\mathrm{of}\mathrm{neutrons}$

Atomic Number (Z):

• It is the no.of protons present in the nuclei of an atom.
• Since the Helium atom has 2 protons in its nuclei, its atomic number, Z=2.

Isotopes:

• These are the species that have the same atomic number but a different mass number.
• For example: $\mathrm{Carbon}-12,\mathrm{Carbon}-13\mathrm{and}\mathrm{carbon}-14$

Given:

$\mathrm{Protons}=6\left(\mathrm{X}\right):6\left(\mathrm{Y}\right)$

$\mathrm{Neutrons}=6\left(\mathrm{X}\right):8\left(\mathrm{Y}\right)$

For atomic specie $\mathrm{X}$:

$$\begin{gathered} \mathrm{Mass}\mathrm{number}=\mathrm{Number}\mathrm{of}\mathrm{protons}+\mathrm{Number}\mathrm{of}\mathrm{neutrons} \\ \mathrm{Mass}\mathrm{number}=6+6 \\ \mathrm{Mass}\mathrm{number}=12 \end{gathered}$$

For atomic specie $\mathrm{Y}$:

$$\begin{gathered} \mathrm{Mass}\mathrm{number}=\mathrm{Number}\mathrm{of}\mathrm{protons}+\mathrm{Number}\mathrm{of}\mathrm{neutrons} \\ \mathrm{Mass}\mathrm{number}=6+8 \\ \mathrm{Mass}\mathrm{number}=14 \end{gathered}$$

Relation between X and Y:

• The mass number of $\mathrm{X}$ and $\mathrm{Y}$ is 12 and 14 respectively.
• These two atomic species, $\mathrm{X}$ and $\mathrm{Y}$ have the same atomic number i.e. 6 but different mass numbers. So, they are isotopes of each other.