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Engineering Mathematics
Probability & Statistics
GATE 2010
Medium

The Maxwell-Boltzmann velocity distribution for the x-component of the velocity, at temperature T, is f(vx)=√(m/(2πkT))·exp(−mvx²/(2kT)). The standard deviation of the distribution is

  • A√(2kT/m)
  • BkT/m
  • √(kT/m)
  • DkT/2m

Explanation

Matching to the standard normal form (1/(σ√(2π)))exp(−vx²/(2σ²)): 1/(2σ²)=m/(2kT) ⟹ σ²=kT/m ⟹ σ=√(kT/m).

Source: GATE CH 2010 (2010)

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