Correct order of radius of the first orbit of `H, He^+, Li^(2 +), Be^(3 +)` is :

Options

A. `H gt He^(+) gt Li^(2+) gt Be^(3+)`
B. `Be^(3+) gt Li^(2+) gt He^(+) gt H`
C. `He^(+) gt Be^(3+) gt Li^(2+) gt H`
D. `He^(+) gt H gt Li^(2+) gt Be^(3+)`

Answer

To determine the correct order of the radius of the first orbit for the ions \( H \), \( He^+ \), \( Li^{2+} \), and \( Be^{3+} \), we need to consider the relationship between the charge of the nucleus (number of protons) and the number of electrons in the orbit. The radius of the orbit decreases as the positive charge of the nucleus increases, due to the stronger attraction between the nucleus and the electrons.

### Step-by-Step Solution:

1. **Identify the ions and their charges:**
- Hydrogen (\( H \)): 1 proton, 1 electron
- Helium ion (\( He^+ \)): 2 protons, 1 electron
- Lithium ion (\( Li^{2+} \)): 3 protons, 1 electron
- Beryllium ion (\( Be^{3+} \)): 4 protons, 1 electron

2. **Understand the relationship between charge and radius:**
- The radius of the orbit decreases with increasing positive charge (number of protons) because the nucleus pulls the electrons closer as the charge increases.
- Since all these ions have only one electron, the effective nuclear charge experienced by that electron increases with the number of protons.

3. **Rank the ions based on their effective nuclear charge:**
- \( H \) has the least positive charge (1 proton), so it has the largest radius.
- \( He^+ \) has 2 protons, so it has a smaller radius than \( H \).
- \( Li^{2+} \) has 3 protons, so it has a smaller radius than \( He^+ \).
- \( Be^{3+} \) has 4 protons, so it has the smallest radius.

4. **Write the order of the radii from largest to smallest:**
- The order of the radius from largest to smallest is:
\[ H > He^+ > Li^{2+} > Be^{3+} \]

### Final Answer:
The correct order of the radius of the first orbit of \( H, He^+, Li^{2+}, Be^{3+} \) is:
\[ H > He^+ > Li^{2+} > Be^{3+} \]