1000 dust particles are trapped on a surface. There are two energy levels the particles can be in: absorbed on the surface in a zero energy state, or excited with energy E1. At a certain temperature T0, the particles are in thermal equilibrium, and 20 % of the particles are in the excited state. What is the ratio of the total energy of the dust particles to kT0?
To find the ratio of the total energy of the dust particles to kT0, we need to consider the energy levels and the distribution of particles at a certain temperature.
Let's assume there are N dust particles in total. If 20% of the particles are in the excited state, that means 0.2N particles are in the excited state, and the remaining 0.8N particles are in the absorbed state.
The total energy of the dust particles can be calculated by multiplying the number of particles in each state by their respective energies and adding them together.
The energy of particles in the excited state (E1) is given by E1 * (0.2N). Similarly, the energy of particles in the absorbed state (0 energy) is given by 0 * (0.8N). Adding these energy contributions, the total energy of the dust particles is:
Etotal = E1 * 0.2N + 0 * 0.8N = E1 * 0.2N.
Now, let's consider the definition of kT0, where k is the Boltzmann constant and T0 is the temperature. The term kT0 represents the average thermal energy of particles at temperature T0. Hence, kT0 can be considered as a unit of energy.
To get the ratio of the total energy of the dust particles to kT0, we divide the total energy by kT0:
Etotal / kT0 = (E1 * 0.2N) / kT0.
Therefore, the ratio of the total energy of the dust particles to kT0 is (E1 * 0.2N) / kT0.