The principal quantum number of n of an atomic orbitals is `5` what are the posible values of l ?

Explanation

To find the possible values of the azimuthal quantum number (l) when the principal quantum number (n) is given as 5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Quantum Numbers**:
- The principal quantum number (n) indicates the main energy level of an electron in an atom.
- The azimuthal quantum number (l) defines the shape of the orbital and can take on integer values.

2. **Determine the Range for l**:
- The values of l range from 0 to (n - 1).
- This means that for a given value of n, l can take on multiple values.

3. **Apply the Formula**:
- Given n = 5, we can calculate the maximum value for l:
\[ l = 0, 1, 2, 3, \ldots, (n - 1) \]
- Therefore, substituting n = 5:
\[ l = 0, 1, 2, 3, 4 \]

4. **List the Possible Values**:
- The possible values of l when n = 5 are:
- l = 0 (s orbital)
- l = 1 (p orbital)
- l = 2 (d orbital)
- l = 3 (f orbital)
- l = 4 (g orbital)

### Final Answer:
The possible values of l when the principal quantum number n is 5 are: **0, 1, 2, 3, 4**.

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