molecules have 'rms' velocity 2km/s. The 'rms' velocity of the oxygen molecules at same temperature is.

Options

A. 2km/s
B. 8km/s
C. 0.5km/s
D. 1km/s

Explanation

To find the RMS velocity of oxygen molecules at the same temperature given that the RMS velocity of hydrogen molecules is 2 km/s, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The RMS velocity (\( V_{RMS} \)) of a gas is given by the formula:
\[ V_{RMS} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the universal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas.

2. **Proportionality at Constant Temperature**: At the same temperature, the RMS velocities of different gases are inversely proportional to the square root of their molar masses. This can be expressed as:
\[ \frac{V_{RMS, H_2}}{V_{RMS, O_2}} = \sqrt{\frac{M_{O_2}}{M_{H_2}}} \]

3. **Identify Molar Masses**: The molar mass of hydrogen (\( H_2 \)) is approximately 2 g/mol, and the molar mass of oxygen (\( O_2 \)) is approximately 32 g/mol.

4. **Substituting Values**: We know that the RMS velocity of hydrogen is given as 2 km/s. Therefore, we can substitute the values into the equation:
\[ \frac{2 \text{ km/s}}{V_{RMS, O_2}} = \sqrt{\frac{32 \text{ g/mol}}{2 \text{ g/mol}}} \]

5. **Calculate the Square Root**: Simplifying the right side:
\[ \sqrt{\frac{32}{2}} = \sqrt{16} = 4 \]

6. **Rearranging the Equation**: Now we can rearrange the equation to find \( V_{RMS, O_2} \):
\[ V_{RMS, O_2} = \frac{2 \text{ km/s}}{4} = 0.5 \text{ km/s} \]

7. **Final Result**: Thus, the RMS velocity of oxygen molecules at the same temperature is:
\[ V_{RMS, O_2} = 0.5 \text{ km/s} \]

### Final Answer:
The RMS velocity of the oxygen molecules at the same temperature is **0.5 km/s**.