91Ó°ÊÓ

Electrical excitation, in which the initial electron absorbs the energy of another, more energetic electron, can also excite electrons.

A quantized system with three discrete energy levels 0,1.5, and 4 eV has been created. An electron collides with that system with a kinetic energy of 2 eV. We're curious if the electron's energy is adequate to stimulate the system. This excitation can happen if the following conditions are met:

$\text{Energy of the electron}â‰\yen {\mathrm{Δ·¡}}_{\mathrm{ij}}(\mathrm{i}≠\mathrm{j})$

The energy differential between the I and j energy levels in that system is called ${\mathrm{Δ·¡}}_{\mathrm{ij}}.$Because we have three states, all of the energy differences we have are proportional to the number of states.

$$\begin{gathered} {\mathrm{Δ·¡}}_{12}=1.5\mathrm{eV}−0\mathrm{eV}=1.5\mathrm{eV} \\ \text{(satisfies the excitation condition}2\mathrm{eV}>1.5\mathrm{eV}\text{)} \\ {\mathrm{Δ·¡}}_{13}=4\mathrm{eV}−0\mathrm{eV}=4\mathrm{eV} \\ \text{(doesn't satisfy the excitation condition}2\mathrm{eV}â‰\pm 1.5\mathrm{eV}\text{)} \\ {\mathrm{Δ·¡}}_{23}=4\mathrm{eV}−1.5\mathrm{eV}=3.5\mathrm{eV} \\ \text{(doesn't satisfy the excitation condition}2\mathrm{eV}â‰\pm 3.5\mathrm{eV}\text{)} \end{gathered}$$

The electron can excite the system from the first to the second energy level as a result of the previous calculations since its kinetic energy is greater than the difference in energies between levels 1 and 2.

The kinetic energy of an electron is 0.5.

The system we have, which in our instance is the atom, absorbs an amount of energy equal to $∆{\mathrm{E}}_{12}$, and the electron's kinetic energy after collision is as follows: