Question

For a system of particles in thermal equilibrium, what is the probability that a particle will have energy greater than \( E_0 \) according to the Boltzmann distribution?

• A. \( e^{-\frac{E_0}{kT}} \)
• B. \( 1 - e^{-\frac{E_0}{kT}} \)
• C. \( e^{\frac{E_0}{kT}} \)
• D. \( 1 + e^{\frac{E_0}{kT}} \)

Hint:

The Boltzmann distribution describes the probability of a system's particle having a particular energy. The probability decreases exponentially with energy, and the partition function \( Z \) is used to normalize the distribution.