Question

The atomic and molecular rms speeds of gases, Vrms, are usually quite large, even at low temperatures.What is Vrms, in meters per second, for helium atoms at 5.4 K (which is close to the point of liquefaction)?

Answer 1

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.

Answer 2

The average atomic and molecular rms speeds, or Vrms, of gases are quite large even at low temperatures. The Vrms for helium atoms at 5.4 K, close to the point of liquefaction, can be calculated using the formula: Vrms = √((3kT)/(m)), where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the helium atom.

Step-by-step explanation:

The average atomic and molecular rms speeds, or Vrms, of gases are quite large even at low temperatures. The Vrms for helium atoms at 5.4 K, close to the point of liquefaction, can be calculated using the formula:

Vrms = √((3kT)/(m))

where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the helium atom. For helium, the mass is approximately 6.646 x 10^-27 kg.

Using this formula, we can calculate the Vrms for helium atoms at 5.4 K.