Given:
Radius of hydrogen atom in ground state = 0.53 Å

To find:
Radius of Li2+ ion in a similar state

Solution:
In order to find the radius of Li2+ ion, we need to understand the concept of atomic radius and the factors that affect it.

1. Atomic Radius:
The atomic radius is defined as the distance between the nucleus of an atom and its outermost electron. It is usually measured in picometers (pm) or angstroms (Å).

2. Factors Affecting Atomic Radius:
The atomic radius of an atom depends on various factors such as:
- Number of protons in the nucleus: As the number of protons increases, the attractive force between the protons and electrons increases, leading to a decrease in atomic radius.
- Number of electron shells: As the number of electron shells increases, the atomic radius also increases because the electrons are farther away from the nucleus.
- Effective nuclear charge: The effective nuclear charge is the net positive charge experienced by the outermost electrons. As the effective nuclear charge increases, the atomic radius decreases.

3. Comparison between Hydrogen and Li2+ ion:
- Hydrogen atom (atomic number = 1) has one proton in its nucleus and one electron in its outermost shell. The radius of the hydrogen atom in the ground state is given as 0.53 Å.
- Li2+ ion (atomic number = 3) is formed by the loss of two electrons from a lithium atom. It has three protons in its nucleus and only one electron in its outermost shell.

4. Reasoning:
- Since Li2+ ion has one less electron than hydrogen atom, the effective nuclear charge experienced by the outermost electron in Li2+ ion is higher than that in the hydrogen atom.
- As the effective nuclear charge increases, the atomic radius decreases.
- Therefore, the radius of Li2+ ion in a similar state is expected to be smaller than the radius of the hydrogen atom.

5. Answer:
Option A: 0.17 Å is the correct answer as it represents a smaller atomic radius for the Li2+ ion compared to the hydrogen atom.