The ratio of the angular momentum of the orbital electron in the first orbit to that in the 2nd orbital is

Options

A. `2:1`
B. `1:1`
C. `1:2`
D. `2:3`

Answer

To find the ratio of the angular momentum of the orbital electron in the first orbit to that in the second orbit, we can follow these steps:

### Step 1: Understand the formula for angular momentum
The angular momentum (L) of an electron in an orbit is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where:
- \( n \) is the principal quantum number (orbit number)
- \( h \) is Planck's constant

### Step 2: Calculate angular momentum for the first orbit (n=1)
For the first orbit (n=1):
\[ L_1 = 1 \cdot \frac{h}{2\pi} = \frac{h}{2\pi} \]

### Step 3: Calculate angular momentum for the second orbit (n=2)
For the second orbit (n=2):
\[ L_2 = 2 \cdot \frac{h}{2\pi} = \frac{2h}{2\pi} = \frac{h}{\pi} \]

### Step 4: Find the ratio of angular momentum in the first orbit to that in the second orbit
Now, we need to find the ratio \( \frac{L_1}{L_2} \):
\[ \frac{L_1}{L_2} = \frac{\frac{h}{2\pi}}{\frac{2h}{2\pi}} \]

### Step 5: Simplify the ratio
When we simplify the ratio:
\[ \frac{L_1}{L_2} = \frac{h}{2\pi} \cdot \frac{2\pi}{2h} = \frac{1}{2} \]

### Conclusion
Thus, the ratio of the angular momentum of the orbital electron in the first orbit to that in the second orbit is:
\[ \frac{L_1}{L_2} = \frac{1}{2} \]

### Final Answer
The answer is \( \frac{1}{2} \).

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