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 solve the problem of finding the radius of the nth orbit of a hydrogen atom given the radius of the first orbit (R), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**: According to Bohr's model of the hydrogen atom, the radius of the nth orbit (Rn) is given by the formula:
\[ R_n = \frac{0.529 \, n^2}{Z} \text{ angstroms} \]
where \( n \) is the principal quantum number (orbit number) and \( Z \) is the atomic number.

2. **Identify the Values**: For hydrogen (H), the atomic number \( Z = 1 \). Therefore, the formula simplifies to:
\[ R_n = 0.529 \, n^2 \text{ angstroms} \]

3. **Relate to the First Orbit**: The radius of the first orbit (R1) is:
\[ R_1 = 0.529 \, (1^2) = 0.529 \text{ angstroms} \]
In the problem, it is given that this value is equal to \( R \).

4. **Express Rn in Terms of R**: Since \( R = 0.529 \text{ angstroms} \), we can express \( R_n \) in terms of \( R \):
\[ R_n = 0.529 \, n^2 = R \cdot n^2 \]

5. **Final Expression**: Thus, the radius of the nth orbit can be expressed as:
\[ R_n = R \cdot n^2 \]

### Conclusion:
The radius of the nth orbit of the hydrogen atom is \( R \cdot n^2 \).