The surface of the sun has a temperature of about 6.0 103 K. This hot gas contains hydrogen atoms (m = 1.67 10-27 kg). Find the rms speed of these atoms.
Somewhere in your course materials you should find the equation
Vrms = sqrt(3*k*T/m)
where k is the Boltzmann constant, 1.38*10^-23 J/K . It is equal to the molar gas constant R divided by Avogadro's number.
To find the rms (root mean square) speed of the hydrogen atoms in the hot gas of the sun, you can use the equation:
v = √(3kT/m),
where:
- v is the rms speed of the atoms,
- k is the Boltzmann constant (1.38 × 10^-23 J/K),
- T is the temperature in Kelvin,
- m is the mass of the atoms.
In this case, the temperature of the sun's surface (T) is given as 6.0 × 10^3 K, and the mass of a hydrogen atom (m) is approximately 1.67 × 10^-27 kg.
Plugging in these values into the equation, we can calculate the rms speed of the hydrogen atoms:
v = √(3 * (1.38 × 10^-23 J/K) * (6.0 × 10^3 K) / (1.67 × 10^-27 kg))
≈ √(2.76 × 10^-19 J / 1.67 × 10^-27 kg)
≈ √(1.65 × 10^8)
≈ 4.06 × 10^4 m/s.
Therefore, the rms speed of the hydrogen atoms in the hot gas of the sun is approximately 4.06 × 10^4 m/s.