Energy of the dust

Classical Mechanics Level 3

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.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.