Orbital angular momentum depends on .........

Options

A. `l`
B. `n` and `l`
C. `n` and `m`
D. `m` and `s`

Explanation

To determine what orbital angular momentum depends on, we can follow these steps:

### Step 1: Understand Orbital Angular Momentum
Orbital angular momentum is a property of electrons in an atom that describes the momentum associated with their motion around the nucleus. It is quantified by the azimuthal quantum number (L).

### Step 2: Recall the Formula
The formula for calculating orbital angular momentum (L) is given by:
\[ L = \sqrt{l(l + 1)} \frac{h}{2\pi} \]
Where:
- \( l \) is the azimuthal quantum number (also referred to as the orbital quantum number).
- \( h \) is Planck's constant.

### Step 3: Identify the Variables
From the formula, we can see that:
- The term \( h/2\pi \) is a constant and does not affect the dependence of angular momentum on other variables.
- The variable \( l \) (the azimuthal quantum number) directly influences the value of orbital angular momentum.

### Step 4: Analyze the Options
Now, let's analyze the options given in the question:
1. **L** - This refers to the azimuthal quantum number, which we identified as crucial for determining angular momentum.
2. **N and L** - While N (the principal quantum number) is important for defining the energy level, it does not directly affect angular momentum.
3. **N and M** - M (the magnetic quantum number) also does not directly influence the calculation of angular momentum.
4. **M and S** - S (the spin quantum number) is related to electron spin, not orbital motion.

### Step 5: Conclusion
Based on the analysis, we conclude that orbital angular momentum primarily depends on the azimuthal quantum number \( L \).

### Final Answer
The correct answer is **Option A: L**.

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