A: All Cr-o bond length in `K_(2)Cr_(2)O_(7)` are equal
R: Both the Cr are present in `dsp^(2)` hybrid state

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, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that "All Cr-O bond lengths in K2Cr2O7 are equal."

1. **Understanding K2Cr2O7**: This compound is potassium dichromate, which contains the dichromate ion (Cr2O7)²⁻.
2. **Structure of Cr2O7²⁻**: In the dichromate ion, chromium is in a +6 oxidation state. The structure consists of two chromium atoms bonded to seven oxygen atoms.
3. **Bonding and Resonance**: The Cr-O bonds can exhibit resonance due to the presence of double bonds and single bonds. The oxygen atoms can share their lone pairs, leading to multiple resonance structures.
4. **Bond Lengths**: In the Cr2O7²⁻ ion, three of the Cr-O bonds are equivalent due to resonance, while the other bonds have different characteristics. Therefore, not all Cr-O bond lengths are equal.

**Conclusion**: The assertion is **false**.

### Step 2: Analyze the Reason
The reason states that "Both the Cr are present in dsp² hybrid state."

1. **Hybridization of Chromium**: To determine the hybridization, we first find the oxidation state of chromium in K2Cr2O7. The oxidation state is +6.
2. **Electron Configuration**: The electron configuration of chromium in the +6 state is [Ar] 3d⁰ 4s⁰, indicating that both the 3d and 4s orbitals are empty.
3. **Hybridization**: In the case of Cr2O7²⁻, the hybridization is not dsp². The hybridization involves the 3d orbitals and the 4s orbital, leading to a different hybridization state (likely sp³ or sp³d).
4. **Conclusion**: The reason provided is also **false**.

### Final Conclusion
Both the assertion and the reason are false. Therefore, the correct option is the one that states both the assertion and reason are false.

### Answer
The correct option is **4**: Both assertion and reason are false.

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