In Cr - atom the number of 3d - electron having spin quantum number , s = + `1/2` are

Options

A. 10
B. 5
C. 2
D. 1

Answer

To solve the question regarding the number of 3d electrons in a chromium atom that have a spin quantum number of +1/2, we can follow these steps:

### Step 1: Determine the Electronic Configuration of Chromium
The electronic configuration of chromium (Cr) is given as:
\[ \text{Cr: } [\text{Ar}] 3d^5 4s^1 \]

### Step 2: Identify the 3d Electrons
From the electronic configuration, we see that chromium has 5 electrons in the 3d subshell.

### Step 3: Understand the Spin Quantum Number
The spin quantum number (s) can have two values: +1/2 and -1/2. Electrons in the same orbital will have opposite spins due to the Pauli exclusion principle. However, if there are multiple orbitals (like in the case of 3d), each orbital can hold one electron with spin +1/2 before pairing occurs.

### Step 4: Distribute the 3d Electrons
In the 3d subshell, the 5 electrons will occupy the five available orbitals (3dxy, 3dyz, 3dzx, 3dx²-y², and 3dz²) singly before any pairing occurs. Therefore, each of these 5 electrons will have a spin quantum number of +1/2.

### Step 5: Count the Electrons with Spin +1/2
Since all 5 electrons in the 3d subshell have a spin quantum number of +1/2, the total number of 3d electrons with spin +1/2 is:
\[ \text{Total} = 5 \]

### Conclusion
Thus, the number of 3d electrons in a chromium atom that have a spin quantum number of +1/2 is **5**.