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. `4.77`
B. `1.06`
C. `0.13`
D. `2.12`

Answer

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**: The radius of the stationary states of the hydrogen atom is given by the formula:
\[ R_n = a_0 \times n^2 \]
where \( R_n \) is the radius for the principal quantum number \( n \), \( a_0 \) is the Bohr radius for \( n=1 \), and \( n \) is the principal quantum number.

2. **Identify the Values**: We know from the problem statement that:
- \( a_0 = 0.53 \, \text{Å} \) (the radius for \( n=1 \))
- We need to find \( R_2 \) (the radius for \( n=2 \)).

3. **Substitute the Values into the Formula**: For \( n=2 \):
\[ R_2 = a_0 \times (2^2) \]

4. **Calculate \( 2^2 \)**:
\[ 2^2 = 4 \]

5. **Multiply by \( a_0 \)**:
\[ R_2 = 0.53 \, \text{Å} \times 4 \]

6. **Perform the Multiplication**:
\[ R_2 = 2.12 \, \text{Å} \]

7. **Conclusion**: The radius of the first excited state (n=2) is approximately \( 2.12 \, \text{Å} \).

### Final Answer:
The radius of the first excited state (n=2) is approximately **2.12 Å**.

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