Find the rms speed of hydrogen molecules at room temperature `( = 300 K)`.

Explanation

To find the root mean square (RMS) speed of hydrogen molecules at room temperature (300 K), we can follow these steps:

### Step 1: Write down the formula for RMS speed
The formula for the RMS speed (v_rms) of gas molecules 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 in kilograms per mole.

### Step 2: Identify the values needed for the calculation
- The universal gas constant \( R = 8.31 \, \text{J/(mol K)} \).
- The temperature \( T = 300 \, \text{K} \).
- The molar mass of hydrogen \( M = 2 \, \text{g/mol} = 2 \times 10^{-3} \, \text{kg/mol} \).

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the RMS speed formula:
\[ v_{rms} = \sqrt{\frac{3 \times 8.31 \, \text{J/(mol K)} \times 300 \, \text{K}}{2 \times 10^{-3} \, \text{kg/mol}}} \]

### Step 4: Calculate the numerator
First, calculate the numerator:
\[ 3 \times 8.31 \times 300 = 7473 \, \text{J/mol} \]

### Step 5: Calculate the entire expression under the square root
Now, divide this result by the molar mass:
\[ \frac{7473}{2 \times 10^{-3}} = 3736500 \, \text{m}^2/\text{s}^2 \]

### Step 6: Take the square root
Now take the square root to find the RMS speed:
\[ v_{rms} = \sqrt{3736500} \approx 1933.7 \, \text{m/s} \]

### Step 7: Round the result
Rounding this to two decimal places, we have:
\[ v_{rms} \approx 1.93 \times 10^3 \, \text{m/s} \]

### Final Answer
The RMS speed of hydrogen molecules at room temperature (300 K) is approximately:
\[ \boxed{1.93 \times 10^3 \, \text{m/s}} \]