**Question:**

In a group of molecules all traveling in the positive z direction, what is the probability that a molecule will be found with a z-component speed between 400 and 401 m/s if m/(2kT ) = 5.62 × 10^{−6} s^{2} /m^{2} ? (Hint: You need to find and normalize a one-dimensional distribution function first!)

**Solution:**

According to the Boltzmann distribution law, the probability of finding a molecule with an energy ε_{z} in this group of molecules, is proportional to,

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