On the basis of Bohr’s model, the radius of the `3^("rd")` orbit is :

Options

A. equal to the radius of first orbit
B. three times the radius of first orbit
C. five times the radius of first orbit
D. nine times the radius of first orbit

Explanation

To find the radius of the 3rd orbit based on Bohr's model, we can follow these steps:

### Step 1: Understand the Formula
According to Bohr's model, the radius of the nth orbit (R_n) is given by the formula:
\[ R_n = \frac{0.53 \times n^2}{Z} \text{ angstroms} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (orbit number),
- \( Z \) is the atomic number of the element.

### Step 2: Substitute the Values
For the 3rd orbit, we have:
- \( n = 3 \)

Substituting \( n \) into the formula:
\[ R_3 = \frac{0.53 \times (3^2)}{Z} \text{ angstroms} \]

### Step 3: Calculate \( n^2 \)
Calculate \( n^2 \):
\[ n^2 = 3^2 = 9 \]

### Step 4: Substitute \( n^2 \) into the Formula
Now substitute \( n^2 \) back into the equation:
\[ R_3 = \frac{0.53 \times 9}{Z} \text{ angstroms} \]
\[ R_3 = \frac{4.77}{Z} \text{ angstroms} \]

### Step 5: Relate \( R_3 \) to \( R_1 \)
From the formula for the first orbit \( R_1 \):
\[ R_1 = \frac{0.53 \times 1^2}{Z} = \frac{0.53}{Z} \text{ angstroms} \]

Now, we can express \( R_3 \) in terms of \( R_1 \):
\[ R_3 = 9 \times R_1 \]

### Final Answer
Thus, the radius of the 3rd orbit is:
\[ R_3 = 9 \times R_1 \]