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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