If r is 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 the hydrogen atom in terms of the radius of the first orbit (r), we can use the formula derived from Bohr's model of the atom. Here's the step-by-step solution:

### Step 1: Understand the formula for the radius of the nth orbit
According to Bohr's model, the radius of the nth orbit (R_n) of a hydrogen atom can be expressed as:
\[ R_n = \frac{0.529 \, n^2}{Z} \, \text{angstroms} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (the orbit number),
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)).

### Step 2: Substitute the values for hydrogen
For hydrogen, the atomic number \( Z \) is 1. Therefore, the formula simplifies to:
\[ R_n = 0.529 \, n^2 \, \text{angstroms} \]

### Step 3: Find the radius of the first orbit
The radius of the first orbit (n = 1) is given as:
\[ R_1 = 0.529 \, \text{angstroms} \]
This can be denoted as \( r \):
\[ r = 0.529 \, \text{angstroms} \]

### Step 4: Express the radius of the nth orbit in terms of r
Now, we can express the radius of the nth orbit in terms of r:
\[ R_n = 0.529 \, n^2 = r \cdot n^2 \]

### Conclusion
Thus, the radius of the nth orbit of the hydrogen atom can be expressed as:
\[ R_n = r \cdot n^2 \]