Assertion: In `Cr_2O_7^(2-)` ion, all the `Cr-O` bond lengths are equal.
Reason: In `Cr_2O_7^(2-)` ion all the `O-Cr-O` bond angles are equal.

Options

A. If both (A) and (R) are correct and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct, but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect but (R) is incorrect.

Explanation

To solve the question regarding the assertion and reason about the `Cr_2O_7^(2-)` ion, let's break it down step by step.

### Step 1: Analyze the Assertion
The assertion states that in the `Cr_2O_7^(2-)` ion, all the `Cr-O` bond lengths are equal. To evaluate this, we need to consider the structure of the dichromate ion.

- The `Cr_2O_7^(2-)` ion has a specific structure where two chromium atoms are bonded to seven oxygen atoms.
- In this structure, there are both single and double bonds between chromium and oxygen. Specifically, there are two `Cr=O` double bonds and five `Cr-O` single bonds.

**Conclusion for Step 1:** Since there are different types of bonds (single and double), the bond lengths cannot be equal. Therefore, the assertion is **incorrect**.

### Step 2: Analyze the Reason
The reason states that in the `Cr_2O_7^(2-)` ion, all the `O-Cr-O` bond angles are equal.

- The `Cr_2O_7^(2-)` ion has a symmetrical structure. The bond angles around each chromium atom are influenced by the arrangement of the surrounding oxygen atoms.
- In the case of the `Cr_2O_7^(2-)` ion, the geometry is such that the `O-Cr-O` bond angles are indeed equal due to the symmetrical arrangement of the oxygen atoms around the chromium atoms.

**Conclusion for Step 2:** The reason is **correct**.

### Final Conclusion
- The assertion is **incorrect**.
- The reason is **correct**.

Thus, the correct answer to the question is that the assertion is false while the reason is true.