Answer :

To understand why Barium (Ba) has a larger atomic radius than Magnesium (Mg), we need to examine their positions and properties in the periodic table.

1. Periodic Table Position:
- Barium (Ba) and Magnesium (Mg) are both found in Group 2 of the periodic table, known as the alkaline earth metals.

2. Electron Shells and Periods:
- Magnesium (Mg) is located in Period 3 of the periodic table. This means Magnesium has three electron shells.
- Barium (Ba) is located in Period 6. This means Barium has six electron shells.

3. Effect of Electron Shells on Atomic Radius:
- As you move down a group in the periodic table, each successive element has an additional electron shell.
- More electron shells mean the outermost electrons are further away from the nucleus.

4. Atomic Radius:
- The atomic radius is defined as half the distance between the nuclei of two adjacent atoms.
- More electron shells result in an increase in the atomic size because the outer electrons are less tightly bound to the nucleus due to increased shielding by inner electrons.

Therefore, Barium, with its six electron shells, has a much larger volume compared to Magnesium, which only has three electron shells. Essentially, the atomic radius increases down a group as the number of electron shells increases, causing the atoms to be larger.

In conclusion, Barium (Ba) has a larger atomic radius than Magnesium (Mg) because Barium has more electron shells, placing its outermost electrons further from the nucleus, resulting in a larger atomic size.