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."

- K₂Cr₂O₇ (Potassium dichromate) contains the dichromate ion (Cr₂O₇²⁻).
- In the dichromate ion, there are two chromium (Cr) atoms and seven oxygen (O) atoms.
- The structure of the dichromate ion is such that it has a resonance structure, which means that the bond lengths can vary due to the different arrangements of electrons.
- Upon examining the bond lengths, we find that there are two types of Cr-O bonds: one type is longer (approximately 179 pm) and the other is shorter (approximately 163 pm).
- Therefore, the assertion that all Cr-O bond lengths are equal is **false**.

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

- To determine the hybridization of chromium in K₂Cr₂O₇, we need to consider the oxidation state of Cr, which is +6.
- In this state, Cr has the electronic configuration of [Ar] 3d⁵ 4s².
- In the presence of oxygen and the formation of the dichromate ion, the hybridization involves the d, s, and p orbitals.
- The correct hybridization for Cr in K₂Cr₂O₇ is actually **d²sp³**, as it involves the participation of two d orbitals, one s orbital, and three p orbitals.
- Therefore, the statement that Cr is in a dsp² hybrid state is also **false**.

### Conclusion
Both the assertion and the reason are false. Therefore, the correct answer is that both statements are incorrect.

### Final Answer
Assertion: False
Reason: False

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