The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature the rms speed of oxygen molecules is v. The rms speed of the hydrogen molecule at the same temperature will be

To find the rms speed of the hydrogen molecule at the same temperature, we can use the concept of the root mean square (rms) speed formula.

The rms speed of a gas molecule is given by the equation:

v = √(3kT/m)

Where:

• v is the rms speed of the molecule
• k is the Boltzmann constant (1.38 x 10^-23 J/K)
• T is the temperature in Kelvin
• m is the mass of the molecule

Given that the mass of an oxygen molecule is about 16 times that of a hydrogen molecule, we can say that the mass of the hydrogen molecule is 1/16th of the mass of the oxygen molecule.

Let's assume the rms speed of the oxygen molecule is v. Now, we need to find the rms speed of the hydrogen molecule at the same temperature.

Using the formula, we can write the equation for the rms speed of the hydrogen molecule as:

v_hydrogen = √(3kT/m_hydrogen)

Since the mass of the hydrogen molecule is 1/16th of the mass of the oxygen molecule, we can substitute m_hydrogen = (1/16)m_oxygen into the equation:

v_hydrogen = √(3kT/(1/16)m_oxygen)

Simplifying the equation, we get:

v_hydrogen = √(48kT/m_oxygen)

Therefore, the rms speed of the hydrogen molecule at the same temperature will be √(48) times the rms speed of the oxygen molecule.