91Ó°ÊÓ

a. We have a quantized system with three discrete energy levels 0, 1.5 and 4 eV . An electron with kinetic energy equals to 2 eV collides with that system. We want to know if that energy, for the electron, is sufficient to excite that system. This excitation can occurs under the following condition:

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

where$\mathrm{Δ}{E}_{ij}$is the energy difference between$i$ and j energy levels in that system. Since we have three states, therefore all energy differences we have are

$\mathrm{Δ}{E}_{12}=1.5eV-0$

localid="1650779325204" $∆E_{13}=4eV-0eV=4eV$

$\mathrm{Δ}{E}_{23}=4eV-1.5eV=3.5eV$ (doesn't satisfy the excitation condition $2eV⪈3.5eV$)

As a result of the above analysis, the electron can excite the system from the first to the second energy level because it has a kinetic energy larger than the difference in energies between level 1 and 2 .

Our system we have which is the atom in our case absorbs an energy equals to $\mathrm{Δ}{E}_{12}$and the electron's kinetic energy after collision becomes as follows

$\mathrm{K}.\mathrm{E}=2\mathrm{eV}-1.5\mathrm{eV}=0.5\mathrm{eV}$