# Why don't electrons stick to the protons in a nucleus?

partialfracti
Positive electrical charges attract negative electrical charges.

The protons in nucleuses (or nucleii? if that's how it's spelled) have positive electrical charges.

Electrons have negative electrical charges.

So why don't electrons stick to the protons in a nucleus instead of orbitting the nucleus?

Gold Member
The explanation for why an electron does not fall into the nucleus comes from a fundamental concept in quantum mechanics: the Heisenberg uncertainty principle. Put simply, it states that you cannot know the position and momentum of a particle simultaneously. More rigorously stated, the product of the uncertainty of the position of a particle (Δx) and the uncertainty of its momentum (Δp) must be greater than a specified value:

$$\Delta x \Delta p \geq \frac{\hbar}{2}$$

Now, as the electron approaches the nucleus, it's uncertainty in position decreases (if the electron is 10nm away from the nucleus, it could be anywhere within a spherical shell of radius 10nm, but if the electron is only 0.1nm away from the nucleus, that area is greatly reduced). According to the Heisenberg uncertainty principle, if you decrease the uncertainty of the electrons position, the uncertainty in its momentum must increase. This increased momentum uncertainty means that the electron will be moving away from the nucleus faster, on average.

Put another way, if we do know that at one instant, that the electron is right on top of the nucleus, we lose all information about where the electron will be at the next instant. It could stay at the nucleus, it could be slightly to the left or to the right, or it could very likely be very far away from the nucleus. Therefore, because of the the uncertainty principle it is impossible for the electron to fall into the nucleus and stay in the nucleus.

In essence, the uncertainty principle causes a sort of quantum repulsion, that keeps electrons from being too tightly localized near the nucleus.

For further discussion of the issue, you can read through some past threads in PF discussing this issue:

chocofingers
The assumed speed calculated of an electron in the nucleus is higher than the speed of light, which can not be possible practically, thereby, the electron is in its stationary states of an atom!

Staff Emeritus
Positive electrical charges attract negative electrical charges.

The protons in nucleuses (or nucleii? if that's how it's spelled) have positive electrical charges.

Electrons have negative electrical charges.

So why don't electrons stick to the protons in a nucleus instead of orbitting the nucleus?

You should also start by reading the FAQ thread in the General Physics forum.

Zz.

michaelc187
got to be Heat

because at absolute zero -it is stuck...

thats all i know

got to be Heat

because at absolute zero -it is stuck...

thats all i know

I hope for your sake it isn't all you know, since it's very wrong.

The states of electrons in an atom do not change with temperature. All that changes is which state they're in, and an electron is neither stationary nor very near the nucleus when it's in its lowest-energy (ground) state. And at room temperature, they're almost entirely in their electronic ground states anyway.

NEILS BOHR
and then there's somethin called BINDING ENERGY as well...

mack_10
One of the first problems considered in quantum mechanics

Perhaps it is better to think of the wave nature of the electron in this instance instead of the particle nature, can a wave collapse to a point?

Nakisima
In essence, the uncertainty principle causes a sort of quantum repulsion, that keeps electrons from being too tightly localized near the nucleus.

So the electrons are orbiting so fast they're kept in a sort of perpetual "slingshot", in that the nucleus is attracting the electrons, but they can neither be completely attracted to, nor catapulted away from the nucleus because of their velocity?

northernbear
quantum mechanics explains why electrons do not stick to the nucleus

per quantum mechanics, electrons are only allowed certain descrete energy states. electrons are not allowed to have energy states in between, above, or below the perscribed energy states of the orbitals. therefore, electrons are confined to to the energy states of the orbitals.
sticking to the nucleus is an energy state not allowed for electrons, therefore, electrons do not "fall" into the nucleus

in classical physics, a world of falling apples and bouncing billard balls, the electron would fall into the nucleus. at our scale of things, in our world, where quantum effects are too small for us to notice, without sophisticated measurements, and if we thought of electrons as the size of charged billard balls, the negatively charged "billard ball" would move until it stuck to the positively charged "billard ball," ie all positions and potential energy states are allowed for the billard balls in classical physics. however, electrons are not billard balls. in an electron's world and scale of things, quantum effects are a big factor, and although the laws of classical physics would allow an electron to move and stick to the proton, the laws of quantum physics do not allow an electron to have the low potential energy state that it would have stuck to the nucleus, therefore the electron cannot be stuck to the nucleus

Gold Member
So the electrons are orbiting so fast they're kept in a sort of perpetual "slingshot", in that the nucleus is attracting the electrons, but they can neither be completely attracted to, nor catapulted away from the nucleus because of their velocity?

No, because of the uncertainty principle, it is incorrect to think of electrons as having a trajectory. Moving in a trajectory implies that both the position and momentum are known, forbidden by the uncertainty principle (for more discussion, see my post here). Rather, you have to think about describing an electrons position in terms of probabilities of where it will be (a probability distribution) and its movement as how this probability distribution changes over time.

If you were to create a state where the electron was tightly localized to the nucleus (high probability of finding the electron at the nucleus, low probability of finding it elsewhere), this state would not be stable. The probability distribution would quickly evolve to a state where the electron is much less tightly localized around the nucleus.

dreiter
and then there's somethin called binding energy as well...

omg we have neils bohr on the forum!1!11!

Phrak
Then there are the times the electrons do 'stick', re. K electron capture.

Nakisima
No, because of the uncertainty principle, it is incorrect to think of electrons as having a trajectory.

TV programmes should really stop using the classic "electrons orbiting a nucleus" type animation then.

Gold Member
Unfortunately it is difficult to visualize the behavior of quantum mechanical particles.

Macocio
What about the nearby protons, they might pull the electrons slightly away from the nucleans. Just as the moon pulls on Earth's water.

Just a hypothesis

Staff Emeritus
What about the nearby protons, they might pull the electrons slightly away from the nucleans. Just as the moon pulls on Earth's water.

Just a hypothesis

This is why one ends up with either a "bond", or a hybrid orbital!

Really, there's no need to make "hypothesis". This is one of the most studied and well-known areas of quantum mechanics. We can only hope that people try to learn what we already know!

Zz.

Macocio
This is why one ends up with either a "bond", or a hybrid orbital!

Really, there's no need to make "hypothesis". This is one of the most studied and well-known areas of quantum mechanics. We can only hope that people try to learn what we already know!

Zz.

You mean that the electron bond is caused by my previous statement?

Staff Emeritus