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 problem of determining the number of 3d electrons in a chromium (Cr) atom that have a spin quantum number of +1/2, we can follow these steps:

### Step 1: Determine the Atomic Number of Chromium
Chromium has an atomic number of 24. This means it has 24 electrons in its neutral state.

**Hint:** The atomic number of an element tells you the number of protons and, in a neutral atom, the number of electrons.

### Step 2: Write the Electron Configuration
The electron configuration of chromium can be written as follows:
- The electron configuration generally follows the order of filling according to the Aufbau principle.
- For chromium, the expected configuration would be [Ar] 3d^4 4s^2. However, due to stability reasons, one electron from the 4s orbital is promoted to the 3d orbital.

Thus, the actual electron configuration of chromium is:
\[ \text{Cr: } [\text{Ar}] 3d^5 4s^1 \]

**Hint:** Remember that some transition metals exhibit exceptions to the expected electron configurations for stability.

### Step 3: Identify the 3d Electrons
From the electron configuration [Ar] 3d^5 4s^1, we can see that there are 5 electrons in the 3d subshell.

**Hint:** The notation "3d^5" indicates that there are 5 electrons in the 3d subshell.

### Step 4: Determine the Spin Quantum Number
Each electron can have one of two spin quantum numbers: +1/2 or -1/2. According to Hund's rule, electrons will fill degenerate orbitals (those of the same energy) singly before pairing up.

In the case of the 3d subshell:
- There are 5 orbitals in the 3d subshell.
- Each of the 5 electrons will occupy a separate orbital with a spin of +1/2 before any pairing occurs.

**Hint:** Hund's rule states that electrons will fill each orbital singly with the same spin before pairing up.

### Step 5: Count the Electrons with Spin +1/2
Since all 5 electrons in the 3d subshell have a spin of +1/2, the total number of 3d electrons with a spin quantum number of +1/2 is 5.

**Hint:** If all electrons are unpaired, they all share the same spin quantum number.

### Final Answer
The number of 3d electrons in a chromium atom that have a spin quantum number of +1/2 is **5**.