Step 1: Understanding the Question:
We need to calculate the oxidation state (oxidation number) of the central Chromium (Cr) atom in the compound potassium dichromate.
Step 2: Key Formula or Approach:
The chemical formula for potassium dichromate is $\text{K}_2\text{Cr}_2\text{O}_7$.
The sum of the oxidation states of all atoms in a neutral molecule is always exactly zero.
Standard oxidation states: Potassium (K, an alkali metal) is $+1$, and Oxygen (O) is typically $-2$.
Step 3: Detailed Explanation:
Let the oxidation state of Chromium (Cr) be $x$.
Set up the algebraic equation based on the formula $\text{K}_2\text{Cr}_2\text{O}_7$:
$$2(\text{Oxidation state of K}) + 2(\text{Oxidation state of Cr}) + 7(\text{Oxidation state of O}) = 0$$
Substitute the known values:
$$2(+1) + 2(x) + 7(-2) = 0$$
$$+2 + 2x - 14 = 0$$
$$2x - 12 = 0$$
$$2x = +12$$
$$x = +6$$
Step 4: Final Answer:
The oxidation state of Cr is $+6$, which matches option (B).