The radius of Bohr's first orbit is `a_(0)` . The electron in `n^(th) `orbit has a radius `:`

Options

A. `na_(0) `
B. `a_(0) //n`
C. `n^(2) a_(0)`
D. `a_(0) //n^(2)`

Answer

To find the radius of the electron in the nth orbit according to Bohr's atomic model, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Radius of the First Orbit**:
The radius of the first orbit (n=1) is given as \( a_0 \). This is a known constant in Bohr's model, where \( a_0 \approx 0.529 \) Å (angstroms).

2. **Bohr's Formula for the Radius of the nth Orbit**:
According to Bohr's model, the radius of the nth orbit is given by the formula:
\[ r_n = \frac{n^2 \cdot a_0}{Z} \]
where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (orbit number),
- \( a_0 \) is the radius of the first orbit,
- \( Z \) is the atomic number of the element.

3. **Substituting for the First Orbit**:
For the first orbit (n=1), we have:
\[ r_1 = a_0 \]
This means that when \( n=1 \), the radius is simply \( a_0 \).

4. **Finding the Radius for the nth Orbit**:
Now, we can express the radius for any nth orbit:
\[ r_n = n^2 \cdot \frac{a_0}{Z} \]
This shows that the radius of the nth orbit is proportional to the square of the principal quantum number \( n \).

5. **Conclusion**:
Therefore, the radius of the electron in the nth orbit can be expressed as:
\[ r_n = n^2 \cdot a_0 \]
if we assume \( Z = 1 \) (for hydrogen-like atoms).

### Final Answer:
The radius of the electron in the nth orbit is given by:
\[ r_n = n^2 \cdot a_0 \]