# Energy of the dust

One thousand dust particles are trapped on a surface. The two states that a particle can occupy are

• absorbed on the surface in a zero energy state.
• excited with energy $$E_1$$.

Suppose the particles are in thermal equilibrium at temperature $$T$$, and 20 % of the particles are in the excited state. Find the value of $\frac{1}{k_BT}\sum_i E_i$

Details and Assumptions

• The particles are identical.
• $$k_B$$ is the Boltzmann constant.
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