One the basis of Bohr's model, the radius of the 3rd orbit is :

Options

A. (a) equal to the radius of first orbit
B. (b) three times the radius of first orbit
C. (c) five times the radius of first orbit
D. (d) nine times the radius of first orbit

Answer

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

### Step-by-Step Solution:

1. **Understand Bohr's Model**: According to Bohr's model, the radius of an electron's orbit in a hydrogen-like atom is given by the formula:
\[ r_n = \frac{n^2 \cdot k}{Z} \]
where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (the orbit number),
- \( k \) is a constant,
- \( Z \) is the atomic number of the nucleus.

2. **Identify the Orbit Number**: For the 3rd orbit, we have:
\[ n = 3 \]

3. **Calculate the Radius for the 3rd Orbit**: Plugging \( n = 3 \) into the formula, we get:
\[ r_3 = \frac{3^2 \cdot k}{Z} = \frac{9k}{Z} \]

4. **Calculate the Radius for the 1st Orbit**: For the 1st orbit, where \( n = 1 \):
\[ r_1 = \frac{1^2 \cdot k}{Z} = \frac{k}{Z} \]

5. **Determine the Relationship Between the Radii**: Now, we can express \( r_3 \) in terms of \( r_1 \):
\[ r_3 = 9 \cdot r_1 \]

6. **Conclusion**: Therefore, the radius of the 3rd orbit is 9 times the radius of the 1st orbit.

### Final Answer:
The radius of the 3rd orbit is **9 times the radius of the 1st orbit**.

---