In Bohr's model, the atomic radius of the first orbit of Hydrogen atom is `r_(0)` then the radius of the third orbit is

Options

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

Explanation

To solve the problem of finding the radius of the third orbit of a hydrogen atom in Bohr's model, we can follow these steps:

### Step 1: Understand the formula for the radius of orbits in Bohr's model
In Bohr's model, the radius of the nth orbit of a hydrogen atom is given by the formula:
\[ R_n = R_0 \cdot n^2 \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( R_0 \) is the radius of the first orbit (given as \( R_0 \)),
- \( n \) is the principal quantum number (the orbit number).

### Step 2: Identify the value of \( n \) for the third orbit
For the third orbit, the principal quantum number \( n \) is 3.

### Step 3: Substitute \( n \) into the formula
Using the formula from Step 1, we can substitute \( n = 3 \):
\[ R_3 = R_0 \cdot (3^2) \]

### Step 4: Calculate \( R_3 \)
Now, we calculate \( 3^2 \):
\[ 3^2 = 9 \]
So, substituting this back into the equation gives:
\[ R_3 = R_0 \cdot 9 \]

### Step 5: Write the final answer
Thus, the radius of the third orbit is:
\[ R_3 = 9 R_0 \]

### Conclusion
The radius of the third orbit of the hydrogen atom in Bohr's model is \( 9 R_0 \).

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