In terms of Bohr radius `a_(0)`, the radius of the second Bohr orbit of a hydrogen atom is given by

Options

A. `4a_(0)`
B. `8a_(0)`
C. `sqrt2a_(0)`
D. 2 `a_(0)`

Answer

To find the radius of the second Bohr orbit of a hydrogen atom in terms of the Bohr radius \( a_0 \), we can follow these steps:

### Step 1: Understand the formula for the radius of the nth Bohr orbit
The radius of the nth Bohr orbit is given by the formula:
\[ R_n = a_0 \cdot \frac{n^2}{Z} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( a_0 \) is the Bohr radius,
- \( n \) is the principal quantum number (orbit number),
- \( Z \) is the atomic number of the hydrogen atom (which is 1).

### Step 2: Substitute the values for the second Bohr orbit
For the second Bohr orbit, we have \( n = 2 \) and for hydrogen, \( Z = 1 \). Therefore, we can substitute these values into the formula:
\[ R_2 = a_0 \cdot \frac{2^2}{1} \]

### Step 3: Calculate \( R_2 \)
Now, calculate \( R_2 \):
\[ R_2 = a_0 \cdot \frac{4}{1} = 4a_0 \]

### Conclusion
Thus, the radius of the second Bohr orbit of a hydrogen atom is:
\[ R_2 = 4a_0 \]