What is likely to be orbit number for a circular orbit of diameter `20 nm` of the hydrogen atom:

Options

A. `10`
B. `14`
C. `12`
D. `16`

Explanation

To determine the orbit number for a circular orbit of diameter 20 nm in a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Diameter**:
The diameter of the circular orbit is given as \( D = 20 \, \text{nm} \).

2. **Calculate the Radius**:
The radius \( r \) of the orbit is half of the diameter:
\[ r = \frac{D}{2} = \frac{20 \, \text{nm}}{2} = 10 \, \text{nm} \]

3. **Convert Radius to Meters**:
To work in standard SI units, convert nanometers to meters:
\[ r = 10 \, \text{nm} = 10 \times 10^{-9} \, \text{m} \]

4. **Use Bohr's Model Formula**:
According to Bohr's model, the radius of the nth orbit for hydrogen is given by:
\[ r_n = \frac{0.529 \, n^2}{Z} \, \text{Å} \]
where \( Z \) is the atomic number. For hydrogen, \( Z = 1 \).

5. **Convert Radius to Angstroms**:
Since \( 1 \, \text{nm} = 10 \, \text{Å} \), we convert the radius:
\[ r = 10 \, \text{nm} = 10 \times 10 \, \text{Å} = 100 \, \text{Å} \]

6. **Set Up the Equation**:
Now we can set up the equation using the radius we calculated:
\[ 100 = \frac{0.529 \, n^2}{1} \]

7. **Solve for \( n^2 \)**:
Rearranging the equation gives:
\[ n^2 = \frac{100}{0.529} \]
Calculating this gives:
\[ n^2 \approx 189.03 \]

8. **Calculate \( n \)**:
Taking the square root to find \( n \):
\[ n \approx \sqrt{189.03} \approx 13.7 \]

9. **Round to Nearest Whole Number**:
Since \( n \) must be a whole number, we round 13.7 to the nearest whole number:
\[ n \approx 14 \]

10. **Conclusion**:
Therefore, the likely orbit number for the hydrogen atom with a circular orbit of diameter 20 nm is \( n = 14 \).

### Final Answer:
The orbit number is approximately **14**.