Question

What is the typical speed of a helium atom in a child’s balloon at 20°C room temperature?

Answer 1

The expression for the RMS speed is,

\(v_{r m c}=\sqrt{\frac{3 R T}{M}}\)

Here, \(M\) is the molar mass.

The molar mass of the helium is,

\(M=4 \times 10^{-3} \mathrm{~kg}\)

The temperature is,

\(\begin{aligned} T &=20^{\circ} \mathrm{C}+273.15 \mathrm{~K} \\ &=293.15 \mathrm{~K} \end{aligned}\)

Substitute, the values in the above equation.

\(v_{r m}=\sqrt{\frac{3(8.314 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K})(293.15 \mathrm{~K})}{4 \times 10^{-3} \mathrm{~kg}}}\)

\(=1352 \mathrm{~m} / \mathrm{s}\)

Hence, the speed of the helium atom in the child's balloon is \(v_{r m s}=1352 \mathrm{~m} / \mathrm{s}\)