# Which electron gets which energy level?

Electrons sit in different energy levels of an atom, the farther the higher energy is. Every electrons have the same structure, they can gain energy from environment, electrons which gained energy could jump to a higher energy level and will finally fall back again.

I'm wondering why some electrons have the "right" to "store" that high energy since every electron is the same. Why do those electrons can have more energy and sit in higher energy level than other electrons?

• I'm trying to clarify my question. Let me say, in sodium atom. 1s2,2s2,2p6,3s1, the energy of electrons increases from 1s to 3s. So, I wanna ask that every electrons have the same structure, but they can sit in different energy level, what determines the electron 1 to go to the 1s, electron 2 go to 3s – user40003 Feb 6 '14 at 19:40

The electron is not who "wins" energy. The increase in energy corresponds to the system electron-nucleus. The "incoming" energy is stored in the system, by increasing the distance from the nucleus to the electron.
The configuration of the atom, is such that always "looking" the lowest energy state for the system.

Pauli's exclusion Principle requires no two electrons to occupy the same quantum state. Based on spin, it is decided which electron 'sits' where it does. As far as the 'jumping' to the higher energy is concerned, it depends on the way the electron gains energy. If say, light of energy which matched the energy difference between two energy level is incident, then the electrons 'jump' to that energy level.

I'm surprised that no one has mentioned that there is really no such thing as "this electron" or "that electron" in an atom. Those are useful approximations that help us visualize energy levels; but the actual quantum-mechanical theory of, for example, a carbon atom with six electrons, is based on a single electron wave function in 18-dimensional phase space.

Or look at a Helium atom if you prefer, with only two electrons. You cannot solve for the wave function of the first excited state by saying "one electron is in the s-state and the other one is in the p-state." You have to write a function in six-dimensional wave space, and it has to be symmetrical in both electrons...so that if you switch "them" around, it's exactly the same function except for a 180 degree phase change.

• I don't know about wave function much. So, basically what you are saying we can't count electrons in an atom? But in chemical reaction, we count how many electrons the atom gains or gives away. And in Pauli's principle, we count how many electrons occupy the orbit. – user40003 Feb 7 '14 at 15:50
• We can count the total number of electrons in an atom; but we can't EXACTLY count how many are an "orbital", because the idea of discrete orbitals is only a good approximation that helps us do chemistry.There really is just one big wave function for all the electrons in the atom.The common explanation of the Pauli principle makes it look like we just put two electrons in each orbital, but the correct technical definition of the Pauli principle is that if we reverse any two "electrons" the 3n-dimensional wave function, we get the same wave function back again except with a negative sign. – Marty Green Feb 8 '14 at 2:50
• so what's valence electrons? – user40003 Feb 8 '14 at 17:11

"I'm wondering why some electrons have the "right" to "store" that high energy".
Take a read of energy levels in Bohr's model. Since electron can only revolve in certain orbits they will be at a certain distance from the nucleus. They all will have different kinetic and potential energies.
Electron store different energies because they are having different electrostatic potential(determined by the distance from the nuclues) energy and different kinetic energy(determined by their speed).
your arguments should be the other way round, that is:

Different electrons have different energies because they sit in different energy level.

Edit: It should be understood that velocity of an electron revolving in a circular orbit depends upon the radius of the orbit.
Since the motion of electron is considered as circular the acceleration of the electron is constant and can be found easily as: $F=m_ea$
Also The coloumb's force is $F=\dfrac{Z k_{e} e^2}{r^2}$

Also for uniform circular motion $a=v{\dfrac{d\theta }{dt}}=v\omega ={\dfrac {v^{2}}{r}}$
So $\dfrac{m_\mathrm{e} v^2}{r} = \dfrac{Zk_\mathrm{e} e^2}{r^2}$
$\implies \dfrac{1}{2}m_ev^2=\dfrac{1}{2} \dfrac{Zk_\mathrm{e} e^2}{r}$

hence $K.E=\dfrac{1}{2} \dfrac{Zk_\mathrm{e} e^2}{r}$
Note: The signs have their usual meaning. Kinetic energy is calculated for the unrelativistic case i.e. $v<<c$.

• That's what I'm asking, why electrons with the same structures could sit in different energy levels. In a stable atom, certain electrons sit in certain levels, what make electrons to only show up in that are of cloud? – user40003 Feb 6 '14 at 19:33
• So what cause them on different energy level? I understand the difference between potential energy, what about kinetic energy(speed)? – user40003 Feb 7 '14 at 1:50
• @user40003 Click on the link given in my answer and ask what you do not understand in it. Remember in bohr's model different orbits have different radius. Total energy in a circular orbit = K.E + P.E = $E= {1\over 2} m_\mathrm{e} v^2 - {Z k_\mathrm{e} e^2 \over r} = - {Z k_\mathrm{e} e^2 \over 2r}.$ – user31782 Feb 7 '14 at 6:40

The electrons are indistinguishable, so whenever you do any real calculation you should treat EVERY electron on equal footing.

So indeed your claim of saying:

I'm wondering why some electrons have the "right" to "store" that high energy since every electron is the same. Why do those electrons can have more energy and sit in higher energy level than other electrons?

Is justified! The correct way of doing this, is by working in Fock-space where every electron is treated the same way.

So as @Tinchito correctly notices, you should look at the SYSTEM, and not at single electrons.