Rankers Physics

Atomic Structure: Practice Problem & Solution

In which of the following systems will be radius of the first orbit (n = 1) be minimum: (2003)
Doubly ionised lithium
Singly ionised helium
Deuterium atom
Hydrogen atom

Solution Explained:

To solve this problem, we apply the core principles of Atomic Structure. Understanding the underlying formula is key to arriving at the correct answer below:

The radius of the nth orbit in a hydrogen-like species is given by $r_n \propto \frac{n^2}{Z}$. For the first orbit ($n=1$), the radius is inversely proportional to the atomic number $Z$. Doubly ionised lithium ($Li^{2+}$) has the maximum $Z=3$, thus it has the minimum radius.

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