A: `Cr_(2)O_(7)^(-2)`, is orange in colour
R: It is due to the presence of unpaired electrons in d-subshell of Cr.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question regarding the assertion and reason related to the color of \( \text{Cr}_2\text{O}_7^{2-} \), we will break it down step by step.

### Step 1: Analyze the Assertion
The assertion states that \( \text{Cr}_2\text{O}_7^{2-} \) is orange in color. This is a well-known fact in chemistry, as the dichromate ion is indeed orange.

**Hint**: Research the common colors of transition metal compounds to verify the assertion.

### Step 2: Determine the Oxidation State of Chromium
To understand the reason for the color, we need to calculate the oxidation state of chromium in \( \text{Cr}_2\text{O}_7^{2-} \).

1. Let the oxidation state of chromium be \( x \).
2. Oxygen has an oxidation state of -2, and there are 7 oxygen atoms, contributing a total of \( -14 \).
3. The overall charge of the dichromate ion is -2.

Setting up the equation:
\[ 2x + (-14) = -2 \]
\[ 2x - 14 = -2 \]
\[ 2x = 12 \implies x = +6 \]

**Hint**: Remember that the sum of oxidation states must equal the overall charge of the ion.

### Step 3: Determine the Electronic Configuration
The electronic configuration of chromium (Cr) is \( [\text{Ar}] 3d^5 4s^1 \). When chromium is in the +6 oxidation state, it loses 6 electrons (5 from 3d and 1 from 4s), leading to:

\[ [\text{Ar}] 3d^0 4s^0 \]

**Hint**: Familiarize yourself with how to determine the electronic configuration of transition metals in different oxidation states.

### Step 4: Analyze the Color Origin
The color of \( \text{Cr}_2\text{O}_7^{2-} \) is not due to unpaired electrons in the d-subshell (since there are none in \( 3d^0 \)). Instead, the orange color arises from a phenomenon known as Ligand to Metal Charge Transfer (LMCT).

In this case, the oxygen (O) donates its lone pair of electrons to the empty d-orbitals of chromium, leading to the absorption of certain wavelengths of light, which results in the observed color.

**Hint**: Understand the concept of LMCT and how it affects the color of transition metal complexes.

### Step 5: Evaluate the Reason
The reason states that the orange color is due to the presence of unpaired electrons in the d-subshell of chromium. Since there are no unpaired electrons in \( \text{Cr}_2\text{O}_7^{2-} \), this reason is incorrect.

### Conclusion
- The assertion is correct: \( \text{Cr}_2\text{O}_7^{2-} \) is orange in color.
- The reason is incorrect: the color is due to LMCT, not unpaired electrons.

Thus, the correct answer is that the assertion is true, but the reason is false.

**Final Answer**: Assertion is true, Reason is false.