Step 1: Understanding the oxidation states of Xenon in XeF\(_4\) and its hydrolysis product.
1. In XeF\(_4\), Xenon is bonded to 4 fluorine atoms.
The oxidation state of xenon in XeF\(_4\) can be calculated using the fact that the oxidation state of fluorine is -1. \[ \text{Oxidation state of Xe in XeF\(_4\)} = 4 \times (-1) = -4 \quad \Rightarrow \quad \text{Oxidation state of Xe} = +4. \] Therefore, the oxidation state of Xe in XeF\(_4\) is +4. 2. When XeF\(_4\) undergoes complete hydrolysis with water, the products formed are Xenon (Xe), Xenon trioxide (XeO\(_3\)), oxygen (O\(_2\)), and hydrofluoric acid (HF): \[ \text{XeF}_4 + \text{H}_2\text{O} \rightarrow \text{Xe} + \text{XeO}_3 + \text{O}_2 + \text{HF} \] In the product XeO\(_3\), Xenon is bonded to three oxygen atoms. The oxidation state of oxygen is -2 in most compounds, so the oxidation state of Xenon can be determined as follows: \[ \text{Oxidation state of Xe in XeO\(_3\)} = 3 \times (-2) = -6 \quad \Rightarrow \quad \text{Oxidation state of Xe} = +6. \] Therefore, the oxidation state of Xenon in XeO\(_3\) is +6.
Step 2: Calculating the difference in oxidation state of Xe.
The oxidation state of Xenon in XeF\(_4\) is +4, and in XeO\(_3\) it is +6. The difference in oxidation state is: \[ 6 - 4 = 2 \] Thus, the difference in oxidation state of Xe between XeF\(_4\) and its oxidized product XeO\(_3\) is 2.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is: