Question

One mole (6.02×10^23 atoms) of helium atoms in the gas phase has 3700 J of microscopic kinetic energy at room temperature. Assume that all atoms move with the same speed. The mass of a helium atom is 6.68×10^−27 kg. What is the speed of a helium atom?

Answer 1

This question involves the concepts of kinetic energy, and rms speed.

The rms speed of helium atom at 5800 K is "1.05 x 10¹⁵ m/s".

We will use the formula of the average kinetic energy of gas molecules to find out the rms speed of the hydrogen atom. rms speed is the root mean square speed of an atom:

$K.E =\frac{1}{2}mv^2\\\\v=\sqrt{\frac{2K.E}{m}}$

where,

v =rms speed = ?

K.E = Kinetic Energy of Helium atoms = 3700 J

m = mass of hydrogen atom = 6.68 x 10⁻²⁷ kg

Therefore,

$v=\sqrt{\frac{2(3700 J)}{6.68\ x\ 10^{-27}\ kg}}$

v = 1.05 x 10¹⁵ m/s

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