Question

Typical molecular speeds (vᵣᵐₛ) are large, even at low temperatures. What is vᵣᵐₛ for helium atoms at 5.00 K, less than one degree above helium’s liquefaction temperature?

a) 71 m/s
b) 91 m/s
c) 110 m/s
d) 128 m/s

Answer 1

The average molecular speed of helium atoms at 5.00 K, just one degree above helium's liquefaction temperature, is approximately 128 m/s.

Step-by-step explanation:

The average molecular speed of helium atoms at 5.00 K, just one degree above helium's liquefaction temperature, can be determined using the root mean square (RMS) speed formula. The RMS speed formula is given by:

VRMS = √((3 * k * T) / M)

Where:

• VRMS is the root mean square speed
• k is the Boltzmann constant (1.38 * 10-23 J/K)
• T is the temperature in Kelvin (5.00 K in this case)
• M is the molar mass of helium (4.0026 g/mol)

Plugging in the given values into the formula:

VRMS = √((3 * 1.38 * 10-23 J/K * 5.00 K) / 4.0026 g/mol)

VRMS ≈ 128 m/s