Q:

I read on this website that there is an infinite number of shells in an atom (at least theoretically). if this is true and to move away from the nucleus requires energy doesnt that implie that an infinte amount of energy is needed for an electron to "escape" an atom. should i be using geometric sequences to explain it?
cheers Peter

- Peter (age 17)

Victoria Australia

- Peter (age 17)

Victoria Australia

A:

Hi Peter,

It's easier to visualize the problem if you work it backwards. Consider the simplest atom, the hydrogen atom. The potential energy of a proton and a far away electron can be taken as zero. As the electron moves closer to the proton it will lose energy by radiation. There is a 'closest' distance of approach, the ground state of the atom, where the electron cannot lose any more energy. The energy value of this state is -13.6 electronVolts. Notice the minus sign; that means the electron is bound and would require energy to remove it. The solution to the Schrödinger equation gives the energy value of the n^{th} state as

E_{n }= -13.6/n^{2}. You are right, there are an infinite number of states available but as n becomes large the total energy of the system goes to zero, i.e. the electron is not bound anymore.

See for more information.

LeeH

Another way to look at the same fact is that if you step up in energy from one level to the next, the steps become smaller and smaller. So after an infinite number of steps you've only gone up a finite energy, 13.6 eV. As you guessed that's similar to (though not quite the same as the behavior of a geometric sequence. E.g. 1/2 +1/4 + 1/8 ... =1, even though it's adding an infinite sequence of numbers.Mike W.

It's easier to visualize the problem if you work it backwards. Consider the simplest atom, the hydrogen atom. The potential energy of a proton and a far away electron can be taken as zero. As the electron moves closer to the proton it will lose energy by radiation. There is a 'closest' distance of approach, the ground state of the atom, where the electron cannot lose any more energy. The energy value of this state is -13.6 electronVolts. Notice the minus sign; that means the electron is bound and would require energy to remove it. The solution to the Schrödinger equation gives the energy value of the n

E

See for more information.

LeeH

Another way to look at the same fact is that if you step up in energy from one level to the next, the steps become smaller and smaller. So after an infinite number of steps you've only gone up a finite energy, 13.6 eV. As you guessed that's similar to (though not quite the same as the behavior of a geometric sequence. E.g. 1/2 +1/4 + 1/8 ... =1, even though it's adding an infinite sequence of numbers.Mike W.

*(published on 04/03/2009)*