# Explanation why dosen't the electron fall into the nucleus?

1. Dec 18, 2005

### pivoxa15

Since the nucleus of an atom is +charged and the electron is -charged, why doesn't at least one electron fall into the nucleus?

2. Dec 18, 2005

### Dr.Brain

Infact you can interpret the sam ein another way. The force that attracts the electron towards the nucleus is the coulomb's force of attraction , therefore when electron is acted upon by this attraction force , it starts falling towards the nucleus in the sense that it keeps failing from taking the straightline path it otherwise would have taken in the absence of external force , thus it on the otherside rotates around the nucleus preserving the minimum quanta of energy it can hold in its state.Since there is a minimum 'quanta of energy' of the atomic orbital the wavefuntion of electron satisfies , it remains in that state and doesnot fall...

3. Dec 18, 2005

### pivoxa15

That was the explanation given by Bohr but that was not an accurate enough picture because the electron dosen't rotate around the nucleus. Bohr couldn't explain the quantised angular momentum which lead to the quantised energy levels either.

4. Dec 18, 2005

### Dr.Brain

What Bohr couldnt explain was that , accelerating electrons radiate EM rays and lose energy , so why dont they end up losing so much energy that they fall into the nucleus .... the appt. answer was given later when the concept of 'quantised energy' states came into picture. As per this , the elctrons can possess only some particular quantised energies which are connected with corresponding orbitals , The elctron in first energy state will have some energy which is particular with that atomic orbital , to reach the second shell , the electron should have some other 'bundle of energy' which will be higher than what it would have in the first shell. So due to quantisation , minimum energy an electron in an orbital can possess would be some finite amount which wouldnt allow it to fall into the nucleus . The electron cannot have energy lower than that 'minimum amount of energy' , which could have allowed it to fall into the nucleus .

BJ

5. Dec 18, 2005

### marlon

I don't understand. Quantisized L and energy are the basic assumption's of Bohr's model. This models "solves" the problems with electrons spiraling down towards the nucleus because of it's basic assumptions it was built from. This model is "wrong" because it assumes that electrons have circular orbits around the nucleus. This clearly contradicts with HUP. But than again, Bohr's model (from 1913) is about 13 years older than Schrödinger's work.

regards
marlon

6. Dec 18, 2005

### cartuz

From history it is known that to this question Born is answers by postulate (or axiom) that electron is not emitting the EM on stationary orbits. It is one of Born's postulates. Later, from quantum theory it is following that the electron is spread on whole orbit around the nuclei because nothing emits EM.
But we can discuss the question. Is it okay with the energy balance of atom in quantum mechanics because we must to consider the relict gravitation fields, I suppose but don't sure.

7. Dec 18, 2005

### pivoxa15

I was trying to say that Bohr couldn't come up with a reason why electrons were quantised in orbitals with quantised angular momentum. He just accepted them as axioms if you like.

What I like to know is what is the current conventional reason given to why electrons does not stick to the nucleus. There is obviously an attractive force between them but what is cancelling this attractive force and keeping the electron from totally "falling" into the nucleus?

8. Dec 18, 2005

### michael879

well I know this isnt the answer your looking for, but forgetting all the quantum stuff, in a newtonian world, the electrons wouldnt all fall into the nucleus either. the ones closer to the nucleus would repel the ones farther away.

9. Dec 18, 2005

### dicerandom

If you do the calculation, classically the electron in a hydrogen atom should fall into the nucleus within a small fraction of a second. The same general idea holds for the inner non-screened electrons in any other atom.

10. Dec 18, 2005

### michael879

yea I know, I was just saying in an atom with a lot of electrons, they wouldnt all fall into the nucleus.

11. Dec 18, 2005

### Suedeos

[random]
at post #2..
so it's kinda like how shuttles are in a constant state of freefall around the earth?
[/random]

12. Dec 18, 2005

### michael879

no... the electrons dont orbit, they can't accelerate because accelerating charges produce light, which would slow the electrons down and they would spiral in to the nucleus.

13. Dec 18, 2005

### Staff: Mentor

An atomic electron has a quantum-mechanical probability distribution which is much larger than the nucleus. This distribution cannot shrink so that it is completely contained inside the nucleus, because of the Heisenberg uncertainty principle.

Nevertheless, the probability distibution is usually not zero inside the nucleus, so there is a small but nonzero probability that the electron can actually be inside the nucleus. In some isotopes, the nucleus can then "capture" the electron and convert a proton to a neutron. This electron capture process has properties similar to beta+ decay, in which the nucleus emits a positron.

14. Dec 18, 2005

### Ratzinger

When an electron is more confined, it has a higher energy spread. Does that imply it is more energetic than a less confined? If so, why are the higher energy orbitals farther away from the nucleus and confine the electron lesser in space (why are higher orbitals larger in space)?
Edit: but wait, energy is quantised in atoms, so why talking about HUP here?

15. Dec 18, 2005

### pivoxa15

I appreciate that everything is a probability with the atom. When you were refering to a small probability that the electron is sticking to the nucleus, you were probably assuming when the electron were in n=1 or higher states.

My question is more, why isn't there an electron state with n=0, that is when the electron is most probably in the nucleus. This state would seem to the most natural for an unexcited electron because of the attractive coloumb force that exists between the electron and proton.

16. Dec 18, 2005

### Staff: Mentor

There is no solution to the Schrödinger equation for hydrogen with n=0. The quantum number n enters into the radial part of the wave function, which is the messiest part of the solution (associated Laguerre polynomials :yuck: ). I haven't looked at the derivation since grad school, and my QM books are at the office, so all I can do right now is guess that n=0 would give you a wave function which is zero everywhere.

In fact, as I recall (again not having my books handy) the n=1 probability distribution does in fact have its maximum value at the origin, i.e. at the nucleus! However, the probability of being within the nucleus also depends on the volume. The volume of the nucleus is very small, so the probability of being inside the nucleus is also small.

If the probability distribution over a volume is constant, then (probability of being inside that volume) = (value of probability distribution) x (volume). If the probability distribution isn't constant, but doesn't change much, then if you take the average value of the probability distribution, this is still a pretty good approximation.

[Note: I'm leaving town tomorrow and won't be back until after Christmas, so someone else will have to answer any further questions.]

17. Dec 18, 2005

### Staff: Mentor

Remember, the HUP connects position and momentum. More specifically, it connects corresponding vector components: $x$ with $p_x$, etc. It's quite possible for $p_x$, $p_y$ and $p_z$ to vary (or be uncertain) while the kinetic energy remains constant. Also, the (total) energy includes potential energy, which certainly varies with position for an atomic electron.

So there's no problem with atomic states having a definite fixed energy. What they can't have is a definite fixed momentum.

18. Dec 19, 2005

### Dr.Brain

And as far as I remember the wavefuction of the only electron in Hydrogen atom permits electron being inside the nucleus. That is for r=0 the exponential function converges to zero. Please correct me if anyone knows the exavt wavefucntion expression.

BJ

19. Dec 19, 2005

### pivoxa15

According to the textbook, the most probable distance the electron is from the nucleus in the ground state of H is 0.529(10^-10)m

This is very far compared with the diameter of a nucleus which is of the order of (10^-15)m

The question is still what keeps the electron such a far distance away from the nucleus. Surely it would like to be as close as possible to the nucleus.

20. Dec 19, 2005

### Staff: Mentor

[I have time for one last word while eating breakfast...]

Oddly enough, in the $n=1$ state of hydrogen, the most probable position of the electron is at the origin (the nucleus), whereas the most probable radius is at the Bohr radius $a_0$! This is not a contradiction because there are many more positions that have $r=a_0$ than have $r=0$. Therefore, even though the probability density (square of the wave function) is larger for $r=0$ than for $r=a_0$, the radial probabilty is larger at $r=a_0$. Note the two different names for the quantities!

For the hydrogen wave functions and probability distributions, click here.

And my answer is still: the Heisenberg uncertainty principle.