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 where \( n + l = 7 \), we will follow these steps:

### Step 1: Understand the Quantum Numbers
- The principal quantum number \( n \) can take positive integer values (1, 2, 3, ...).
- The azimuthal quantum number \( l \) can take values from 0 to \( n - 1 \).
- The relationship \( n + l = 7 \) will help us determine the possible values of \( n \) and \( l \).

### Step 2: Determine Possible Values of \( n \) and \( l \)
We need to find combinations of \( n \) and \( l \) such that their sum equals 7:
- If \( n = 7 \), then \( l = 0 \) (7s orbital).
- If \( n = 6 \), then \( l = 1 \) (6p orbital).
- If \( n = 5 \), then \( l = 2 \) (5d orbital).
- If \( n = 4 \), then \( l = 3 \) (4f orbital).

### Step 3: Identify the Maximum Number of Electrons for Each Orbital
Each type of orbital can hold a specific maximum number of electrons:
- **s orbital (l = 0)**: Can hold a maximum of 2 electrons.
- **p orbital (l = 1)**: Can hold a maximum of 6 electrons.
- **d orbital (l = 2)**: Can hold a maximum of 10 electrons.
- **f orbital (l = 3)**: Can hold a maximum of 14 electrons.

### Step 4: Calculate the Total Number of Electrons
Now, we will sum the maximum number of electrons from each of the identified orbitals:
- For 7s: 2 electrons
- For 6p: 6 electrons
- For 5d: 10 electrons
- For 4f: 14 electrons

Total number of electrons:
\[ 2 + 6 + 10 + 14 = 32 \]

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

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