# An unknown atom has the shown energy levels

In an exercise i found, a supposed atom called fictitious (Fi) has the following energy levels:

A) The energies of the emitted photons after a gas of Fi is bombarded with electrons with a kinetic energy of 3.7 eV

B) If Fi is in its ground state, what is the wavelength of the lowest energeric photon it can absorb?

My problem is interpreting the energy levels and get the information I'm suppose to have. Can someone tell me how to use the image?

• When a fast electron is fired at an atom, it can collide with an electron in the atom and some of the KE of the fast electron is transfered to the atomic electron. The fast electron keeps the rest of its KE and continues moving away from the atom after the collision.
• The atomic electron uses this gained energy to move to a higher energy level.
• The electron can only absorb energies exactly equal to the difference in the energy levels between which it moves.

Example: An electron moves from the ground state to the third energy level. $\Delta E$=5.0-3.5=1.5eV, so it must have absorbed 1.5eV of energy. If the electron which was fired at the atom had KE 3.7eV, it must have continued further with 3.7-1.5=2.2eV

• The most amount of energy the electron can receive is 3.7eV (KE of the incoming electron)
• This is enough to move to the -4.0eV, -3.5eV or -2.5eV level but not the top two ones.
• It subsequently returns to its ground energy level, emitting a photon of the energy corresponding to the difference between the levels. This can be 2.5eV, 1.5eV or 1.0eV
• It can also return in more steps rather than straight to the ground state, emitting a photon each time. This can produce photons of energies 0.5ev, 1.0eV and 1.5eV
• You can convert from the photon's energy to its wavelength using the equation $E=hc/\lambda$

You should be able to do B) now as well.

I find this question quite confusing myself, because it is over-simplified. There is a lot which is not explained. However, I think we must interpret the diagram very simply, because that is how it is presented.

I presume that -5.0eV corresponds to the "ground state" (lowest energy level) of the atom and the other levels correspond to the possible energy levels which can be reached from it, 0.0eV corresponding to an electron being freed (unbound) from the atom. The energy levels are negative because energy must be given to the atom to excite it. Absorbing the least energetic photon would excite an atom from the -5.0eV level to the -4.0eV level. I expect you can calculate the wavelength of such a photon (Part B).

Part A is much more complicated, because it involves several issues : partial absoption of energy, absorption followed by emission, and possibly also consecutive absorption/emission events. Part B involves absorption only. Part A also has several possible answers.

The difference between bombardment with electrons instead of photons is that the whole of the electron kinetic energy does not have to be absorbed. So an internal transition (if one occurs) can be less than the KE of the bombarding electron; the remaining KE can be retained by the bombarding electron, or taken up as KE of the whole atom. The atom can be excited to any level which is no more than 3.7eV above the ground level - ie to levels 1, 2 or 3 (counting the ground level as 0). The excited atom then loses energy by emitting one or more photons - ie transitions $3\to 2/1/0$, also $2 \to 1/0$ and $1\to 0$.

A complication is that an excited atom could gain energy from a second bombardment and be excited above level 3 (-2.5eV). Photons can then be emitted from transitions $5 (0.0eV) \to 4/3/2/1/0$ and $4 (-0.5eV) \to 3/2/1/0$. However, you are probably not expected to consider the possibility of a 2nd excitation.

• Right. The only way this can be done, I think, is to assume one electron in the -5.0 eV level. Given the context, evidently an introductory survey, that would be my guess. The important word here being "guess". It seems that the OP found this exercise, and that it is not an assignment. If so, I think he should work the problem with the assumption of one electron in the -5.0 eV state. If not, ask the teacher!! – garyp Jun 7 '16 at 2:01
• @garyp : Good point. The context (resource material) in which the question is found should indicate what assumptions are appropriate here. – sammy gerbil Jun 7 '16 at 2:14
• Very good observations. This problem is not well-defined, since vital information is absent. I think it should only be taken as an exercise on quantized energies and energy transfers. – AlQuemist Aug 16 '17 at 12:02