Find the sum of maximum number of electrons having `+1` and -1 value of 'm' in Ti

Answer

To find the sum of the maximum number of electrons having \( m = +1 \) and \( m = -1 \) values in Titanium (Ti), we will follow these steps:

### Step 1: Determine the Electron Configuration of Titanium
Titanium has an atomic number of 22, which means it has 22 electrons. The electron configuration of Titanium is:
\[ \text{Ti: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^2 \]

### Step 2: Identify the Relevant Orbitals
From the electron configuration, we can see that Titanium has:
- 2 electrons in the 1s orbital
- 2 electrons in the 2s orbital
- 6 electrons in the 2p orbital
- 2 electrons in the 3s orbital
- 6 electrons in the 3p orbital
- 2 electrons in the 4s orbital
- 2 electrons in the 3d orbital

### Step 3: Determine the Magnetic Quantum Number (m) Values
The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \), where \( l \) is the azimuthal quantum number corresponding to the subshell:
- For \( s \) orbitals (\( l = 0 \)): \( m = 0 \)
- For \( p \) orbitals (\( l = 1 \)): \( m = -1, 0, +1 \)
- For \( d \) orbitals (\( l = 2 \)): \( m = -2, -1, 0, +1, +2 \)

### Step 4: Count Electrons for \( m = +1 \) and \( m = -1 \)
- In the **3p** subshell, we have:
- \( m = -1 \): 2 electrons (since there are 6 electrons in 3p, they fill the orbitals according to the Pauli exclusion principle)
- \( m = +1 \): 2 electrons (same reasoning as above)

- In the **3d** subshell, we have:
- \( m = -1 \): 1 electron (there are 2 electrons in 3d, they will occupy the orbitals according to Hund's rule)
- \( m = +1 \): 1 electron (same reasoning as above)

### Step 5: Calculate the Total Electrons for \( m = +1 \) and \( m = -1 \)
- Total electrons for \( m = +1 \):
- From 3p: 2 electrons
- From 3d: 1 electron
- Total for \( m = +1 \): \( 2 + 1 = 3 \)

- Total electrons for \( m = -1 \):
- From 3p: 2 electrons
- From 3d: 1 electron
- Total for \( m = -1 \): \( 2 + 1 = 3 \)

### Step 6: Find the Sum of Electrons for \( m = +1 \) and \( m = -1 \)
Now, we add the total number of electrons for \( m = +1 \) and \( m = -1 \):
\[ \text{Sum} = 3 + 3 = 6 \]

### Final Answer
The sum of the maximum number of electrons having \( +1 \) and \( -1 \) values of \( m \) in Titanium is **6**.

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