An argon atom is released from the surface of the earth to travel upwards at 300 K. Assuming that it — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

Initial kinetic energy of the atom corresponds to its thermal energy. $\frac{1}{2} m v^2 = \frac{3}{2} k_B T$. It travels upwards until all kinetic energy is converted to potential energy: $m g h = \frac{3}{2} k_B T$. Rearranging: $h = \frac{3 k_B T}{2 m g}$. Using molar quantities, $N_A m = M$ and $N_A k_B = R$. So $h = \frac{3 R T}{2 M g}$. Given $R = 8.4\text{ J/K-mol}$, $T = 300\text{ K}$, $M = 40\text{ g/mol} = 0.04\text{ kg/mol}$, $g = 10\text{ ms}^{-2}$. $h = \frac{3 \times 8.4 \times 300}{2 \times 0.04 \times 10} = \frac{7560}{0.8} = 9450\text{ m}$. Therefore, correct answer is 9450.