The orbital configuration of `._(24)Cr` is `3d^(5) 4s^(1)`. The number of unpaired electrons in `Cr^(3+) (g)` is

Options

A. 3
B. 2
C. 1
D. 4

Explanation

To determine the number of unpaired electrons in the chromium ion \( \text{Cr}^{3+} \), we can follow these steps:

### Step 1: Write the Electron Configuration of Chromium
The atomic number of chromium (Cr) is 24. The ground state electron configuration of chromium is:
\[ \text{Cr}: [\text{Ar}] \, 3d^5 \, 4s^1 \]
This indicates that chromium has 5 electrons in the 3d subshell and 1 electron in the 4s subshell.

### Step 2: Determine the Electron Configuration of \( \text{Cr}^{3+} \)
When chromium loses electrons to form \( \text{Cr}^{3+} \), it loses a total of 3 electrons. According to the Aufbau principle, electrons are removed from the outermost shell first. Therefore, we remove the 1 electron from the 4s subshell and 2 electrons from the 3d subshell:
\[ \text{Cr}^{3+}: [\text{Ar}] \, 3d^3 \, 4s^0 \]
This means that the electron configuration for \( \text{Cr}^{3+} \) is \( 3d^3 \).

### Step 3: Determine the Distribution of Electrons in the 3d Subshell
The 3d subshell can hold a maximum of 10 electrons and is made up of 5 orbitals. The 3 electrons in \( \text{Cr}^{3+} \) will occupy the 3d orbitals according to Hund's rule, which states that electrons will fill degenerate orbitals singly before pairing up.

The filling of the 3d orbitals will look like this:
- One electron in the first 3d orbital
- One electron in the second 3d orbital
- One electron in the third 3d orbital

This results in the following configuration:
\[ \text{3d: } \uparrow \, \uparrow \, \uparrow \]
This shows that all three electrons are unpaired.

### Step 4: Count the Number of Unpaired Electrons
From the configuration \( 3d^3 \), we can see that all three electrons are unpaired. Therefore, the number of unpaired electrons in \( \text{Cr}^{3+} \) is:
\[ \text{Number of unpaired electrons} = 3 \]

### Final Answer
The number of unpaired electrons in \( \text{Cr}^{3+} \) is **3**.

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