In Bohr.s model of hydrogen atom, radius of the first orbit of an electron is `r_(0)`. Then, radius of the third orbit is:

Options

A. `(r_(0))/(9)`
B. `r_(0)`
C. `3r_(0)`
D. `9r_(0)`

Answer

To find the radius of the third orbit of an electron in a hydrogen atom according to Bohr's model, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Radius**:
The radius of the nth orbit in a hydrogen atom is given by the formula:
\[ R_n = R_0 \cdot n^2 \]
where \( R_0 \) is the radius of the first orbit and \( n \) is the principal quantum number (the orbit number).

2. **Identify the Values**:
For the hydrogen atom, the atomic number \( Z = 1 \). Thus, we can use the formula directly with \( n \) being the orbit number we are interested in. In this case, we want to find the radius of the third orbit, so we set \( n = 3 \).

3. **Substitute the Value of n**:
Plugging \( n = 3 \) into the formula:
\[ R_3 = R_0 \cdot (3^2) \]

4. **Calculate**:
Now calculate \( 3^2 \):
\[ 3^2 = 9 \]
Therefore:
\[ R_3 = R_0 \cdot 9 = 9R_0 \]

5. **Conclusion**:
The radius of the third orbit \( R_3 \) is \( 9R_0 \).

### Final Answer:
The radius of the third orbit is \( 9R_0 \).

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