Final answer:
The root mean square velocity (Vrms) for helium atoms at 5.4 K is approximately 74.5 m/s.
Step-by-step explanation:
The root mean square velocity (Vrms) represents the average speed of particles in a gas. It is calculated using the equation Vrms = √(3kT/m), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a single particle. For helium atoms at 5.4 K, we can calculate the value of Vrms as follows:
Vrms = √(3kT/m)
First, we need to convert the temperature from Celsius to Kelvin by adding 273.15 K:
T = 5.4 K + 273.15 K = 278.25 K
Next, we need to calculate the mass of a helium atom. The atomic mass of helium is approximately 4 atomic mass units (amu), and 1 amu is equal to 1.661 x 10-27 kg:
m = 4 amu x 1.661 x 10-27 kg/amu = 6.644 x 10-27 kg
Now we can substitute the values into the equation:
Vrms = √(3 x 1.38 x 10-23 J/K x 278.25 K / 6.644 x 10-27 kg)
Simplifying the equation gives us:
Vrms = √(5.557 x 103)
Vrms = 74.5 m/s
Therefore, the root mean square velocity (Vrms) for helium atoms at 5.4 K is approximately 74.5 m/s.