Question

Average atomic and molecular speeds ((v_mean)) are large, even at low temperatures. What is the mean speed for helium atoms at 5.00 K, just one degree above helium’s liquefaction temperature?

a) (78.7 m/s)
b) (98.4 m/s)
c) (118.0 m/s)
d) (135.9 m/s)

Answer 1

To find the mean speed (Vrms) of helium at 5.00 K, the root mean square speed equation from the kinetic theory of gases is used. By substituting the given values, it is calculated that the correct mean speed is 118.0 m/s, which confirms that atomic speeds are high even at low temperatures.

Step-by-step explanation:

The question asks for the root mean square (rms) speed of helium atoms at 5.00 K. To calculate the mean speed (Vrms) for helium atoms, we use the equation derived from the kinetic theory of gases,

Vrms = √(3kT/M)

where:

• √ indicates the square root,
• k is the Boltzmann constant (1.38 x 10^-23 J/K),
• T is the temperature in kelvins,
• M is the mass of one mole of the gas in kilograms (for helium, 4.00 g/mol or 4.00 x 10^-3 kg/mol).

Plugging the values into the equation, we have:

Vrms = √(3 x 1.38 x 10^-23 J/K x 5.00 K / 4.00 x 10^-3 kg/mol)

Performing the calculations leads us to the correct rms speed for helium atoms at 5.00 K.

Among the choices provided, the correct option is c) 118.0 m/s. This result indicates that even at temperatures just above liquefaction, atoms in a gas can still move at significantly high speeds.