An element 'X' present in its ground state, the value of principal annd azimuthal quantum number for last electron of element 'X' is n=3 and l=1 and spin multiplicity for given element is 4. then according to given information correct statement(s) regarding givenn element 'X' is/are:

Options

A. Element 'X' is 3rd period and 15th group element
B. In valence shell of element 'X' electron density is symmetrically distributed
C. Element 'X' has full filled valence shell.
D. none of these

Answer

To solve the problem regarding the element 'X', we need to analyze the given quantum numbers and spin multiplicity, and then derive the electronic configuration and properties of the element.

### Step-by-Step Solution:

1. **Identify Quantum Numbers**:
- Given principal quantum number (n) = 3
- Given azimuthal quantum number (l) = 1 (which corresponds to the p subshell)

2. **Determine Spin Multiplicity**:
- Spin multiplicity is given as 4.
- The formula for spin multiplicity is \(2s + 1\), where \(s\) is the total spin.
- Setting up the equation:
\[ 2s + 1 = 4 \implies 2s = 3 \implies s = \frac{3}{2} \]
- This indicates that there are 3 unpaired electrons (since \(s = \frac{3}{2}\) corresponds to three half spins).

3. **Determine the Electronic Configuration**:
- The last electron is in the 3p subshell, and since there are 3 unpaired electrons, the configuration can be deduced as:
- The complete filling of lower energy levels gives:
\[ 1s^2 2s^2 2p^6 3s^2 3p^3 \]
- Thus, the electronic configuration of element 'X' is \(1s^2 2s^2 2p^6 3s^2 3p^3\).

4. **Identify the Period and Group**:
- From the electronic configuration, we can see that element 'X' is in the 3rd period (due to n=3).
- To find the group, we count the valence electrons:
- Valence electrons = \(2 (from \, 3s) + 3 (from \, 3p) = 5\)
- Elements in the p-block with 5 valence electrons belong to group 15.

5. **Analyze the Statements**:
- **Statement A**: "Element X is in the third period and 15th group."
- This is **correct** based on our findings.
- **Statement B**: "In the valence shell of element X, electron density is symmetrically distributed."
- This is also **correct** because the 3p electrons are distributed among the 3px, 3py, and 3pz orbitals.
- **Statement C**: "Element X has a fully filled valence shell."
- This is **incorrect** because there are 3 unpaired electrons in the valence shell.
- **Statement D**: "None of these."
- This is **incorrect** because we have found correct statements A and B.

### Conclusion:
The correct statements regarding element 'X' are:
- Statement A: Element X is in the third period and 15th group.
- Statement B: In the valence shell of element X, electron density is symmetrically distributed.