Among the following orbitals which orbital will have maximum value of orbital angular momentum ?

Options

A. `3s`
B. `4p`
C. `5d`
D. `6f`

Explanation

To determine which orbital has the maximum value of orbital angular momentum, we will follow these steps:

### Step 1: Understand the formula for orbital angular momentum
The formula for calculating the orbital angular momentum (L) is given by:

\[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \]

where \( l \) is the azimuthal quantum number.

### Step 2: Identify the azimuthal quantum numbers for the given orbitals
The azimuthal quantum number \( l \) corresponds to the type of orbital:
- For an s orbital, \( l = 0 \)
- For a p orbital, \( l = 1 \)
- For a d orbital, \( l = 2 \)
- For an f orbital, \( l = 3 \)

Given the orbitals:
- 3s → \( l = 0 \)
- 4p → \( l = 1 \)
- 5d → \( l = 2 \)
- 6f → \( l = 3 \)

### Step 3: Calculate the values of \( l \) for each orbital
Now we will summarize the azimuthal quantum numbers:
- 3s: \( l = 0 \)
- 4p: \( l = 1 \)
- 5d: \( l = 2 \)
- 6f: \( l = 3 \)

### Step 4: Determine which orbital has the maximum \( l \)
From the values calculated:
- The maximum \( l \) value is for the 6f orbital, where \( l = 3 \).

### Step 5: Conclusion
Since the orbital angular momentum is directly related to the azimuthal quantum number, the orbital with the maximum value of angular momentum is the 6f orbital.

### Final Answer
The orbital with the maximum value of orbital angular momentum is **6f**.

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