# What does it mean when we say an atom has infinite energy levels/shells? [closed]

My chemistry teacher told that an atom has infinite energy shells according to Bohr model , where electron reside according to its angular momentum and energy.

But in lower classes/ grades I have learned that when we give excess energy to atom, the atom loses electron.

But now they are saying that when electron gain energy it move on to higher energy level.

So in this way, an electron should never 'jumps out'(sorry for that word) of atom? And keep going to higher energy levels as atom has infinite energy levels?

And should always be bound with the atom and never lost.

However electrons do actually leave atoms when given excess heat.

So how does atom lose electron and not always being bind with atom when given excess heat in spite of infinite energy levels?

What does my teacher actually mean by saying it?

• The energy levels are not evenly spaced in energy: they get closer and closer. See the little figure here, for an example: chemistry.stackexchange.com/a/119468/79678.
– Ed V
Jul 21 at 17:18
• How many integer numbers n > 0 is there for -a/n^2 < 0 where a is positive real number? Jul 21 at 17:19

Simply put, an electron in a hydrogen atom in a molecule of water in your fingertip could be detected in your elbow, or even on the moon. It does not have a location until detected, only a probability function describing where it can be found.

Raising the energy level changes the probability of where it can be detected, and, as your teacher stated, there are an infinite number of levels. Notice in the energy level diagram at HyperPhysics, or from physicsforums.com, below, that for higher n, levels are closer together. This explains how there can be an infinite number of levels in a finite range of levels. This is a converging infinite series. For example, in Zeno's paradox of Achilles and the tortoise, 1/2 + 1/4 + 1/8... an infinite number of terms never exceeds one.

So, in a sense, even if the hydrogen is in an ionized state, the electron is never completely lost... though it might be indistinguishable from other electrons.

[Irrelevant thought for the day: can atoms be unionized, if they want better working conditions?]

• "an electron in a hydrogen atom in a molecule of water in your fingertip could be detected in your elbow" Strictly speaking, this would require excitation (I'm not sure tunneling to forbidden regions of a potential are possible, that would violate energy conservation?), so that electron is presumably constrained never to be detected in your elbow. Jul 21 at 19:19
• @BuckThorn If the potential is infinite, then the wavefunction is 0, but if it's finite then there is some probability. So it depends on how "forbidden" we're talking. Jul 21 at 19:49
• @orthocresol good point. But how do you circumvent the issue with conservation of energy? "Quantum tunneling allows electrons and other small objects to have a small probability of being in regions where conservation of energy prohibits them." (from web.phys.ksu.edu/vqm/vqmnextgen/qmbasics/…) Hmm, it might be my turn to post a question. Jul 21 at 19:55
• @BuckThorn The act of measuring the particle is what changes its state and thereby its energy. I don't know enough to answer this, but I strongly suspect the question becomes one of how the measurement is done. Measuring the position / momentum / etc. of a particle necessitates its interaction with the measurement apparatus in some way, so you only need the energy of the entire system (particle + measurement apparatus) to be conserved. This is veering into more philosophical, interpretations-of-quantum-mechanics grounds -- en.wikipedia.org/wiki/Measurement_in_quantum_mechanics Jul 21 at 20:06
• @orthocresol yeah, it gets messy. A few posts in physics SE try to answer this, some along the lines of what you propose: physics.stackexchange.com/questions/111697/… Jul 21 at 20:12