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The problem you provided involves calculating the average velocity of a different gas at the same temperature based on the given velocity of oxygen (\(O_2\)) molecules at 0°C. This can be done using **Graham's law of effusion**, which relates the velocities of gases to their molar masses at the same temperature.

### Graham's Law:
\[
\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}
\]
Where:
- \(v_1\) and \(v_2\) are the velocities of gas 1 and gas 2.
- \(M_1\) and \(M_2\) are the molar masses of gas 1 and gas 2.

In this case:
- The velocity of \(O_2\) molecules is given as \(v_1 = 1700 \, \text{km/h}\).
- The molecular mass of \(O_2\) is approximately 32 g/mol (since \(O\) has a molar mass of 16 g/mol and there are 2 oxygen atoms).
- We are asked to find the velocity \(v_2\) of \(UF_3\) at the same temperature.
- The molecular mass of uranium is approximately 232 g/mol, and the molar mass of fluorine is 19 g/mol. So the molecular mass of \(UF_3\) is:
  \[
  M_2 = 232 + 3 \times 19 = 289 \, \text{g/mol}.
  \]

Using these values, we can calculate the velocity of \(UF_3\) molecules using Graham's Law.

Let me calculate that.The velocity of the \(UF_3\) molecules at 0°C is approximately **565.7 km/h**, which matches option **(e)**.

Would you like further details on this calculation or have any additional questions?

Here are some related questions you might find useful:
1. How does Graham's law apply to diffusion and effusion processes?
2. What are the limitations of Graham's law at different temperatures and pressures?
3. How do molecular masses affect the kinetic energies of gases?
4. What are other applications of the kinetic theory of gases in real-world scenarios?
5. How can we experimentally determine the molar mass of a gas?

**Tip:** Graham's law assumes ideal gas behavior, which is a good approximation at high temperatures and low pressures.

Si la velocidad promedio de las moléculas de O2 a 0°C es de 1700 km/h, ¿cuál será la velocidad de las moléculas de UF3 a la misma temperatura?

Calculate the velocity of UF3 gas molecules at 0°C using Graham's law of effusion. The problem compares the velocity of O2 molecules (1700 km/h) with UF3, using the molecular masses of O2 (32 g/mol) and UF3 (289 g/mol).

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