4. The probability that the x-velocity component of particles in a gas lie in the range...

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4. The probability that the x-velocity component of particles in a gas lie in the range V to (v and dv) is P[vx|dvx = Aе-mv²/2kB¹ dux where A = 1/2 m (2TKUT)¹². (i) Explain (without proof) how this result follows directly from the Boltzmann relation, which gives the probability of a state of energy E being occupied, given by P[E] x e-E/k³T. In particular, explain the origins of the exponent and the constant A. [4 marks] 4. The probability that the x-velocity component of particles in a gas lie in the range V to (v and dv) is P[vx|dvx = Aе-mv²/2kB¹ dux where A = 1/2 m (2TKUT)¹². (i) Explain (without proof) how this result follows directly from the Boltzmann relation, which gives the probability of a state of energy E being occupied, given by P[E] x e-E/k³T. In particular, explain the origins of the exponent and the constant A. [4 marks]