The set of quantum numbers n=3, l=0, m=0, s=-1/2 belongs to the element

Options

A. Mg
B. Na
C. Ne
D. F

Explanation

To determine which element corresponds to the given set of quantum numbers (n=3, l=0, m=0, s=-1/2), we can follow these steps:

### Step 1: Identify the Principal Quantum Number (n)
The principal quantum number \( n \) is given as 3. This indicates that the electron is in the third energy level or shell.

**Hint:** The principal quantum number indicates the energy level of the electron in an atom.

### Step 2: Identify the Azimuthal Quantum Number (l)
The azimuthal quantum number \( l \) is given as 0. This corresponds to the s orbital, as \( l = 0 \) represents the s subshell.

**Hint:** The azimuthal quantum number determines the shape of the orbital (s, p, d, f).

### Step 3: Identify the Magnetic Quantum Number (m)
The magnetic quantum number \( m \) is given as 0. For an s orbital, there is only one orientation, which is why \( m \) can only be 0.

**Hint:** The magnetic quantum number specifies the orientation of the orbital in space.

### Step 4: Identify the Spin Quantum Number (s)
The spin quantum number \( s \) is given as -1/2. This indicates that the electron has a spin in the opposite direction (downward spin).

**Hint:** The spin quantum number describes the intrinsic spin of the electron, which can be either +1/2 or -1/2.

### Step 5: Determine the Electron Configuration
Given that we have \( n = 3 \) and \( l = 0 \), we are looking at the 3s orbital. The maximum number of electrons in an s orbital is 2. Since the spin is -1/2, it indicates that this is the last electron being added to the 3s subshell.

### Step 6: Count the Total Electrons
To find the total number of electrons in the atom, we need to consider the filled orbitals before the 3s:
- 1s: 2 electrons
- 2s: 2 electrons
- 2p: 6 electrons
- 3s: 2 electrons

Adding these gives us:
\[ 2 (1s) + 2 (2s) + 6 (2p) + 2 (3s) = 12 \text{ electrons} \]

### Step 7: Identify the Element
The atomic number corresponds to the number of electrons in a neutral atom. An atomic number of 12 corresponds to the element Magnesium (Mg).

**Final Answer:** The element with the quantum numbers \( n=3, l=0, m=0, s=-1/2 \) is Magnesium (Mg).