An electron with 2.00 eV of kinetic energy collides with the atom shown in Figure Ex 38.24.

a. Is the electron able to excite the atom? Why or why not?

b. If your answer to part a was yes, what is the electron’s kinetic energy after the collision?

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:

$\text{Energy of the electron}\ge {\mathrm{\Delta E}}_{\mathrm{ij}}(\mathrm{i}\ne \mathrm{j})$

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

$$\begin{gathered} {\mathrm{\Delta E}}_{12}=1.5\mathrm{eV}-0\mathrm{eV}=1.5\mathrm{eV} \\ \text{(satisfies the excitation condition}2\mathrm{eV}>1.5\mathrm{eV}\text{)} \\ {\mathrm{\Delta E}}_{13}=4\mathrm{eV}-0\mathrm{eV}=4\mathrm{eV} \\ \text{(doesn't satisfy the excitation condition}2\mathrm{eV}\ngeqq 1.5\mathrm{eV}\text{)} \\ {\mathrm{\Delta E}}_{23}=4\mathrm{eV}-1.5\mathrm{eV}=3.5\mathrm{eV} \\ \text{(doesn't satisfy the excitation condition}2\mathrm{eV}\ngeqq 3.5\mathrm{eV}\text{)} \end{gathered}$$

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: