In an orbital electrons are filled according to Aufbau principle, Pauli's exclusion principle and Hund's rule of maximum muliplicity .
According to Aufbau principal the orbital are filled in order to their increasing energies . In the order of increase of energy of orbitals cna be calculated from `( n + l )` rule. Lower the value of `( n + l )` for an orbital the lowest energy hence orbital are filled in order of increasing `( n + l ) ` value. If two orbitals have same `( n + l ) ` value, the orbital with lower value of 'n' has lower energy hence it is filled first.
According to Pauli's exclusion principle, an orbital can have maximum two electrons with opposite spin.
According to Hunds rule pairing of electron in degenerate orbitals of the same sub shell does not take place until each orbital belonging to that sub shell has got one electron each i.e., singly occupied.
If n=4, how many element are possible?

Options

A. 20
B. 14
C. 32
D. 16

Answer

To determine how many elements are possible when \( n = 4 \), we will follow the principles of electron configuration and the rules mentioned in the question.

### Step-by-Step Solution:

1. **Identify the Principal Quantum Number (n)**:
- Given \( n = 4 \), we need to determine the possible values of the azimuthal quantum number \( l \).

2. **Determine the Values of l**:
- The azimuthal quantum number \( l \) can take values from \( 0 \) to \( n - 1 \).
- Therefore, for \( n = 4 \), \( l \) can be \( 0, 1, 2, 3 \).

3. **Identify the Subshells**:
- The corresponding subshells for these \( l \) values are:
- \( l = 0 \) corresponds to the \( 4s \) subshell.
- \( l = 1 \) corresponds to the \( 4p \) subshell.
- \( l = 2 \) corresponds to the \( 4d \) subshell.
- \( l = 3 \) corresponds to the \( 4f \) subshell.

4. **Determine the Number of Orbitals in Each Subshell**:
- The number of orbitals in each subshell is as follows:
- \( 4s \): 1 orbital
- \( 4p \): 3 orbitals
- \( 4d \): 5 orbitals
- \( 4f \): 7 orbitals

5. **Calculate the Maximum Number of Electrons in Each Subshell**:
- Each orbital can hold a maximum of 2 electrons.
- Therefore, the maximum number of electrons in each subshell is:
- \( 4s \): \( 1 \times 2 = 2 \) electrons
- \( 4p \): \( 3 \times 2 = 6 \) electrons
- \( 4d \): \( 5 \times 2 = 10 \) electrons
- \( 4f \): \( 7 \times 2 = 14 \) electrons

6. **Sum the Maximum Number of Electrons**:
- Now, we add the maximum number of electrons from all subshells:
\[ 2 + 6 + 10 + 14 = 32 \]

7. **Conclusion**:
- Therefore, the total number of elements possible when \( n = 4 \) is **32**.

### Final Answer:
The total number of elements possible when \( n = 4 \) is **32**.

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