Question

1. Boltzmann statistics are used to find the distribution or distribution of the velocity of Inert gas at any temperature. If D (v) is the velocity distribution of inert gas at T, then the probability that atoms (or Molecules) of inert gas have velocity in the dv range is equal to D (v) dv, where
D (v) dv = 4π (m / 2πkT) ^ 3⁄2 (v ^ 2) e ^ (- mv2⁄2kT) dv

2.1 Draw the graph between D (v) and v when the inert gas has a temperature of 1000 K (Recommended: Use a program such as Mathematica) to explain. Graph style
2.2 In the Thermosphere atmosphere, which is 100 - 150 km above the earth, the temperature is around 1000 K. Find the probability
Is that the nitrogen gas molecules will escape from gravity. In which the molecules must be faster than the velocity From the earth's surface, which is equal to 11 km / s (recommended: for integration D (v) dv, use the program For example Mathematica)
2.3 The lunar surface velocity is 2.4 km / s. Find the probability that the nitrogen gas molecules will escape from the force. Gravity of the moon And explain that Why does the moon have no atmosphere? (Recommended: set the temperature of the moon's surface to equal1000 K)

Answer 1

velocity distribution :

Temperature T = 1000 K ,

we take m = 23.24 E-27 kg . for the inert gas N-14

exp (-mv²/kT) = exp (-8.42E-7 v²)

D(v) = 9.71E-9 v² exp (-8.42E-7 v²)

2) The probability for velocities more than 3000 m/s or 3 km is almost 0.

The required velocity for N-14 molecules to escape is more than 11km/s.

hence N-molecules cannot escape.

3) N- molecule can escape Moon surface if it has velocity more than 2.4 km/s

from the graph we can see the are under the curve for v >2.4 km/s is non-zero

D(v)*dv = 0.0005*600/2 =  0.15

There is good probability N can escape from Moon's surface and all N has escaped over the years hence no atmosphere over Moon's surface.