The root mean square velocity of hydrogen molecules at 300 K is `1930 ms^(-1)`. The rms velocity of oxygen molecules at 1200 K will be

Options

A. `965 ms^(-1)`
B. `765 ms^(-1)`
C. `1065 ms^(-1)`
D. `865 ms^(-1)`

Explanation

To find the root mean square (RMS) velocity of oxygen molecules at 1200 K, we can use the relationship between RMS velocity, temperature, and molecular weight. The formula for RMS velocity (V_rms) is given by:

\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]

where:
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin,
- \( M \) is the molar mass of the gas.

### Step 1: Understand the relationship between RMS velocities
The RMS velocity is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass. Therefore, we can express the relationship between the RMS velocities of hydrogen and oxygen as:

\[ \frac{V_{rms, O}}{V_{rms, H}} = \sqrt{\frac{T_O}{T_H} \cdot \frac{M_H}{M_O}} \]

### Step 2: Identify the known values
From the question, we know:
- \( V_{rms, H} = 1930 \, \text{m/s} \) (RMS velocity of hydrogen at 300 K)
- \( T_H = 300 \, \text{K} \) (temperature of hydrogen)
- \( T_O = 1200 \, \text{K} \) (temperature of oxygen)
- The molar mass of hydrogen \( M_H = 2 \, \text{g/mol} \)
- The molar mass of oxygen \( M_O = 32 \, \text{g/mol} \)

### Step 3: Substitute the known values into the equation
Now substituting the known values into the equation:

\[ \frac{V_{rms, O}}{1930} = \sqrt{\frac{1200}{300} \cdot \frac{2}{32}} \]

### Step 4: Simplify the equation
Calculating the right side:

1. Calculate the temperature ratio:
\[ \frac{1200}{300} = 4 \]

2. Calculate the mass ratio:
\[ \frac{2}{32} = \frac{1}{16} \]

3. Combine the ratios:
\[ \sqrt{4 \cdot \frac{1}{16}} = \sqrt{\frac{4}{16}} = \sqrt{\frac{1}{4}} = \frac{1}{2} \]

### Step 5: Solve for \( V_{rms, O} \)
Now we can find \( V_{rms, O} \):
\[ V_{rms, O} = 1930 \cdot \frac{1}{2} = 965 \, \text{m/s} \]

### Final Answer
Thus, the RMS velocity of oxygen molecules at 1200 K is:

\[ \boxed{965 \, \text{m/s}} \]