If r is the radius of first orbit, the radius of nth orbit of the H atom will be:

Options

A. `rn^(2)`
B. `rn`
C. `(r)/(n)`
D. `r^(2)n^(2)`

Explanation

To find the radius of the nth orbit of a hydrogen atom given that R is the radius of the first orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Radius**:
The formula for the radius of the nth orbit in a hydrogen atom is given by:
\[ r_n = \frac{0.529 \, n^2}{Z} \, \text{Å} \]
where \( n \) is the principal quantum number (orbit number) and \( Z \) is the atomic number of the element.

2. **Identify the Radius of the First Orbit**:
For the first orbit (where \( n = 1 \)):
\[ R = \frac{0.529 \, (1)^2}{Z} \]
Since hydrogen has an atomic number \( Z = 1 \):
\[ R = \frac{0.529 \, (1)}{1} = 0.529 \, \text{Å} \]

3. **Calculate the Radius for the nth Orbit**:
Now, we want to find the radius for the nth orbit, denoted as \( r_n \):
\[ r_n = \frac{0.529 \, n^2}{Z} \]
Again, since \( Z = 1 \) for hydrogen:
\[ r_n = 0.529 \, n^2 \, \text{Å} \]

4. **Relate the nth Orbit Radius to the First Orbit Radius**:
We can express \( r_n \) in terms of \( R \):
\[ r_n = R \cdot n^2 \]
Since we found that \( R = 0.529 \, \text{Å} \), we can substitute it:
\[ r_n = R \cdot n^2 \]

5. **Conclusion**:
Therefore, the radius of the nth orbit of the hydrogen atom is:
\[ r_n = R \cdot n^2 \]

### Final Answer:
The radius of the nth orbit of the hydrogen atom is given by:
\[ r_n = R \cdot n^2 \]