What is the maximum possible number of electrons in an atom with (n+l=7)

Answer

To find the maximum possible number of electrons in an atom with \( n + l = 7 \), we can follow these steps:

### Step 1: Understand the Quantum Numbers
The principal quantum number \( n \) indicates the energy level of an electron in an atom, while the azimuthal quantum number \( l \) indicates the shape of the orbital. The sum \( n + l \) gives us a specific value, which in this case is 7.

### Step 2: Determine Possible Values of \( n \) and \( l \)
We need to find combinations of \( n \) and \( l \) such that their sum equals 7. The possible values for \( l \) are:
- \( l = 0 \) (s subshell)
- \( l = 1 \) (p subshell)
- \( l = 2 \) (d subshell)
- \( l = 3 \) (f subshell)

Now, we can calculate the corresponding \( n \) values for each \( l \):

1. If \( l = 0 \):
- \( n + 0 = 7 \) → \( n = 7 \)

2. If \( l = 1 \):
- \( n + 1 = 7 \) → \( n = 6 \)

3. If \( l = 2 \):
- \( n + 2 = 7 \) → \( n = 5 \)

4. If \( l = 3 \):
- \( n + 3 = 7 \) → \( n = 4 \)

### Step 3: Calculate Maximum Electrons for Each Combination
Now, we will calculate the maximum number of electrons that can fit into the orbitals corresponding to each combination of \( n \) and \( l \):

1. For \( n = 7, l = 0 \) (s subshell):
- Maximum electrons = 2 (s can hold 2 electrons)

2. For \( n = 6, l = 1 \) (p subshell):
- Maximum electrons = 6 (p can hold 6 electrons)

3. For \( n = 5, l = 2 \) (d subshell):
- Maximum electrons = 10 (d can hold 10 electrons)

4. For \( n = 4, l = 3 \) (f subshell):
- Maximum electrons = 14 (f can hold 14 electrons)

### Step 4: Sum the Maximum Electrons
Now, we sum the maximum number of electrons from all the combinations:

\[ \text{Total maximum electrons} = 2 + 6 + 10 + 14 = 32 \]

### Final Answer
The maximum possible number of electrons in an atom with \( n + l = 7 \) is **32**.

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