The Total spin and magnetic number far the atom with atomic number `24` are

Options

A. `+- 3,sqrt(48) BM`
B. `+- 3,sqrt(35) BM`
C. `+- (3)/(2)sqrt(48) BM`
D. `+- (2)/(3)sqrt(35) BM`

Explanation

To find the total spin and magnetic moment for the atom with atomic number 24 (which is chromium), we will follow these steps:

### Step 1: Determine the Electronic Configuration
The first step is to write the electronic configuration for chromium (atomic number 24). Chromium has an exceptional electron configuration due to its stability with half-filled orbitals. The electronic configuration is:

\[ \text{Cr: } 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^1 \]

### Step 2: Identify Unpaired Electrons
Next, we need to identify the number of unpaired electrons in the electronic configuration.

- In the 3d subshell, there are 5 electrons, which can be arranged as follows: ↑ ↑ ↑ ↑ ↑ (all five electrons are unpaired).
- In the 4s subshell, there is 1 electron which is also unpaired.

Thus, the total number of unpaired electrons is:

\[ \text{Unpaired Electrons} = 5 \, (\text{from } 3d) + 1 \, (\text{from } 4s) = 6 \]

### Step 3: Calculate Total Spin
The total spin \( S \) can be calculated using the formula:

\[ S = \frac{1}{2} \times n \]

where \( n \) is the number of unpaired electrons. Here, \( n = 6 \):

\[ S = \frac{1}{2} \times 6 = 3 \]

### Step 4: Calculate Magnetic Moment
The magnetic moment \( \mu \) can be calculated using the formula:

\[ \mu = \sqrt{n(n + 2)} \]

Substituting \( n = 6 \):

\[ \mu = \sqrt{6(6 + 2)} = \sqrt{6 \times 8} = \sqrt{48} \]

### Final Answer
Thus, the total spin and magnetic moment for the atom with atomic number 24 (chromium) are:

- Total Spin \( S = 3 \)
- Magnetic Moment \( \mu = \sqrt{48} \, \text{B.M.} \)