If `l_(3)andl_(2)` represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then `l_(3):l_(2)` is :

Options

A. `3:2`
B. `9:4`
C. `2:3`
D. `4:9`

Explanation

To solve the problem, we need to find the ratio of the angular momenta \( l_3 \) and \( l_2 \) of an electron in the third and second Bohr orbits, respectively.

### Step-by-Step Solution:

1. **Understand the Formula for Angular Momentum**:
The angular momentum \( l \) of an electron in a Bohr orbit is given by the formula:
\[ l_n = \frac{n h}{2 \pi} \]
where \( n \) is the principal quantum number (the orbit number) and \( h \) is Planck's constant.

2. **Calculate \( l_3 \)**:
For the third Bohr orbit, where \( n = 3 \):
\[ l_3 = \frac{3h}{2 \pi} \]

3. **Calculate \( l_2 \)**:
For the second Bohr orbit, where \( n = 2 \):
\[ l_2 = \frac{2h}{2 \pi} \]

4. **Find the Ratio \( l_3 : l_2 \)**:
To find the ratio \( l_3 : l_2 \), we divide \( l_3 \) by \( l_2 \):
\[ \frac{l_3}{l_2} = \frac{\frac{3h}{2 \pi}}{\frac{2h}{2 \pi}} = \frac{3h}{2 \pi} \times \frac{2 \pi}{2h} \]
Simplifying this gives:
\[ \frac{l_3}{l_2} = \frac{3}{2} \]

5. **Final Result**:
Therefore, the ratio \( l_3 : l_2 \) is:
\[ l_3 : l_2 = 3 : 2 \]