Bohr's radius for the H-atom (n =1) is approximately 0.53 Ã…. The radius of the first excited state (n=2) is :

Options

A. 0.13 Ã…
B. 1.06 Ã…
C. 4.77 Ã…
D. 2.12 Ã…

Explanation

To find the radius of the first excited state (n=2) for the hydrogen atom using Bohr's model, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Bohr Radius**:
The radius of an electron orbit in a hydrogen atom is given by the formula:
\[ R_n = R_0 \cdot n^2 \]
where \( R_n \) is the radius for the nth orbit, \( R_0 \) is the Bohr radius for the ground state (n=1), and \( n \) is the principal quantum number.

2. **Identify the Given Values**:
We know from the question that:
- \( R_0 \) (Bohr radius for n=1) = 0.53 Å
- \( n \) for the first excited state = 2

3. **Calculate the Radius for n=2**:
Substitute the values into the formula:
\[ R_2 = R_0 \cdot (2^2) = 0.53 \, \text{Å} \cdot 4 \]

4. **Perform the Calculation**:
\[ R_2 = 0.53 \, \text{Å} \cdot 4 = 2.12 \, \text{Å} \]

5. **Conclusion**:
Therefore, the radius of the first excited state (n=2) is approximately **2.12 Å**.