The radius of the first orbit of hydrogen in `0.528 overset(0)A`. The radius of second orbit of hydrogen is

Options

A. `4.752 Å`
B. `2.112 Å`
C. `0.071 Å`
D. `0.142 Å`

Answer

To find the radius of the second orbit of a hydrogen atom, we can use Bohr's model of the atom. According to this model, the radius of the nth orbit (Rn) is given by the formula:

\[ R_n = R_1 \cdot n^2 \]

where:
- \( R_1 \) is the radius of the first orbit,
- \( n \) is the principal quantum number (1 for the first orbit, 2 for the second orbit).

### Step-by-Step Solution:

1. **Identify the radius of the first orbit**:
Given that the radius of the first orbit \( R_1 \) is \( 0.528 \, \text{Å} \).

2. **Use the formula for the radius of the nth orbit**:
We need to find the radius of the second orbit \( R_2 \). According to the formula:
\[ R_2 = R_1 \cdot n^2 \]
Here, \( n = 2 \) for the second orbit.

3. **Substitute the values into the formula**:
\[ R_2 = 0.528 \, \text{Å} \cdot 2^2 \]
\[ R_2 = 0.528 \, \text{Å} \cdot 4 \]

4. **Calculate the radius of the second orbit**:
\[ R_2 = 2.112 \, \text{Å} \]

5. **Conclusion**:
Therefore, the radius of the second orbit of hydrogen is \( 2.112 \, \text{Å} \).

### Final Answer:
The radius of the second orbit of hydrogen is \( 2.112 \, \text{Å} \).

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