Question

A nitrogen molecule on surface of earth has a speed equal to rms speed of nitrogen molecule at 0°C. This molecule rises vertically upwards without any collision. What is the height to which it rises. Assume g is constant and equal 9.8 ms^-2. Given 

Mass of nitrogen molecule = 4.65 x 10^-26 kg 

Boltzmann’s constant = k = 1.38 x 10^-23 JK^-1

Answer 1

Let v = v_rms = r.m.s speed of nitrogen molecules

where m is mass of one atom of nitrogen and N_AV is the Avogadro’s number. We know R/N_AV = K = The Boltzmann’s constant. Therefore

Let H be the vertical height to which the nitrogen molecules rises above earth’s surface. Then