The values of four quantum number of valence electron of an element are `n = 4, l = 0, m = 0 and s=+(1)/(2)` . The element is:

Options

A. K
B. Ti
C. Na
D. Sc

Explanation

To determine the element based on the provided quantum numbers \( n = 4, l = 0, m = 0, s = +\frac{1}{2} \), we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 4 \) means that the electron is in the fourth energy level. This corresponds to the fourth period of the periodic table.

**Hint:** The principal quantum number tells you which period the element belongs to.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) describes the shape of the orbital. The value \( l = 0 \) corresponds to an s orbital.

**Hint:** The value of \( l \) determines the type of subshell: \( l = 0 \) is s, \( l = 1 \) is p, \( l = 2 \) is d, and \( l = 3 \) is f.

### Step 3: Identify the Magnetic Quantum Number (m)
The magnetic quantum number \( m \) indicates the orientation of the orbital. Since \( l = 0 \), the only possible value for \( m \) is also \( 0 \). This is consistent with the s orbital, which has no directional properties.

**Hint:** For \( l = 0 \), the only value for \( m \) is 0.

### Step 4: Identify the Spin Quantum Number (s)
The spin quantum number \( s \) indicates the spin of the electron. Here, \( s = +\frac{1}{2} \) indicates that the electron has an upward spin.

**Hint:** The spin quantum number can be either \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

### Step 5: Determine the Element
From the analysis:
- The principal quantum number \( n = 4 \) indicates that the element is in the fourth period.
- The azimuthal quantum number \( l = 0 \) indicates that the electron is in an s orbital.
- Therefore, the valence electron is in the 4s subshell.

The elements in the fourth period that have their valence electrons in the 4s subshell are potassium (K) and calcium (Ca). However, since we are looking for the element with the specified quantum numbers, we focus on potassium (K), which has the electron configuration ending in \( 4s^1 \).

**Final Answer:** The element is Potassium (K).