Question

A hypothetical atom has and energy level structure that obeys the following equation:

Eelectron = -24 eV/n for n = 1,2,3 only.

a) Draw an energy level diagram for the electron in this hypothetical atom, and label the ground state

b) How much energy would be needed, in eV, to excite the atom from the ground state to the second excited state?

c) How much energy would be needed, in eV, to ionize (completely remove an electron from) this hypothetical atom.

Answer 1

a)For an electron, the electronic configuration is 1s2,2s2,2p6,3s2,3p1.
The diagram would look like this:
3p __ __ __
3s __
2p __ __ __
2s __
1s __
You fill in two electrons in each blank, from the bottom to the top (1s through 3s would be completely filled with 12 electrons, and 3p would have a single electron; remember that two electrons in the same orbital, or blank, have opposite spins, up or down).

b)he energy at any given level N = 1/N^2*ground energy
ground energy = level-1 energy = 13.6057 eV or 2.17987E-18 J
To find energy needed to move between levels, take the difference of the two calculated energies.
Thus energy needed to move from level 1 to level 3 = 13.6057(1/1^2-1/3^2) eV or 2.17987E-18(1/1^2-1/3^2) J.
Note that these energies are actually all negative though conventionally shown as positive numbers; they approach 0 as N, and distance, approach infinity.
Thus it takes kinetic energy to move to a higher level even though the higher-level energy is numerically smaller.

c) Formula is E=Ef-Ei

Ef=0 ionization corresponds to E=0
so 0 - (-24)=eV