[Four-digit Integer] An argon atom is released from the surface of the earth to travel upwards at 30 — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

The initial kinetic energy of the argon atom is equal to its average thermal energy: K.E. = 1.5 k_B T. This kinetic energy is converted entirely into gravitational potential energy as it rises: m g h = 1.5 k_B T → M g h = 1.5 R T. Substituting the values: 0.040 kg/mol × 10 m/s^2 × h = 1.5 × 8.4 J/(mol K) × 300 K → 0.40 × h = 3780 → h = 3780 / 0.40 = 9450 m. Thus, the 4-digit answer is 9450.