# Why does electron $(-)$ keep rotating round the nucleus $(+)$ even they are attracted? [duplicate]

I'm a secondary school pupil, my physics textbook discussed atomic physics without deep details because we are young boys, to explain electron motion we first learn about rotational motion. The main problem is that why the electron dose not fall on the nucleus, my textbook said that it doesn't because of centrifugal force, but amazingly I found out in this site that centrifugal force doesn't exist, I told my teacher about this, but he believe that centrifugal force exist, and I will not have any satisfying answer from him. I'm looking for a simple answer (without deep details) that could satisfy such a young asker

## marked as duplicate by user191954, John Rennie, ACuriousMind♦ quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Mar 16 at 9:59

• Regarding "centrifugal force doesn't exist": xkcd.com/123 . Hint: it does exist, but it's a fictitious force. – Ruslan Mar 16 at 10:12
• Why doesn't the moon crash into the Earth? Why don't the planets crash into the sun? – Aaron Stevens Mar 16 at 11:00
• Also don't listen anyone who says that the centrifugal force doesn't exist. It surely exists for anyone in a rotating frame of reference. Don't hold onto anything while going around a sharp curve while driving and then tell me if you think the centrifugal force doesn't exist. – Aaron Stevens Mar 16 at 11:02
• You can also try looking at this page after you have read the answers others gave you: en.m.wikipedia.org/wiki/Bohr_model – Alchimista Mar 16 at 15:17

There are two ways to answer this:

Consider the motion of earth around the sun. Both attract each other due to gravity. Because the sun us much more massive than earth, we can consider it as stationary and ignore the force of the earth acting on the sun.

Now the earth is in circular motion due to the centripetal forceof the sun. Analogy: spin a bucket over your head around a string. You always have to pull towards the center to keep the bucket on a circle. The sun does the same for Earth.

Now, electron and nucleus are similar to earth/sun, they attract due to the electric force. The equations for gravitational and electric forces are "basically the same", so one could argue that also electrons orbit the nucleus the same way as planets orbit the sun.

This is wrong.

There are two problems: electrons are quantum objects and one can not talk about their position in the first place.

Second, charges going in circles would radiate energy, the electron would "fall into the nucleus" almost instantly.

The whole topic of quantum physics is hard and requires a lot of practice to get used to it, but it is necessary to explain stuff at microscopic levels.

To understand this, you have (unfortunately) to completely abandon the idea, that the electron is orbiting the nucleus. You have to accept, that you cannot really track the motion in every detail (not because of measurement, but because of nature).

I will try to give you a short and full explanation without too many details but I have to introduce a weird concept (in the classical sense).

Uncertainty

One of the main results of "quantum mechanics", the theory of really small stuff (which was a revolution 100 years ago), is the so called "uncertainty principle". You can best think of this in the sense of a photograph. Take two pictures of a moving person:

• One time you get a crisp picture of the person. You know really well where the person is located but you cannot say something about the velocity (maybe a bit).
• The second time it is blurred. You just can say, that the person is somewhere around this blurring but not exactly where. On the other side you may be able to track the velocity of the person by the blurring effect.

This is just a methaphor, but it at least explaines this uncertainty principle in some sense. The crucial point: uncertainty in position and velocity are linked! If one of them goes up, the other one goes down.

Now the electron

If it would fall into the nucleus, it would be exactly located at the position of the nucleus. This would raise the uncertainty in velocity, therefore the kinetic energy ($$T=mv^2/2$$) and it would "escape" from the nucleus again (it may sound odd, but perfect knowledge of position would mean an infinite uncertainty in velocity!). Of course, such a situation is prevented (by the same mechanism) before the electron hits the nucleus.

What is the electron doing?

One principle in quantum physics is, that particles like to go into a state, where they have the smallest amount of energy. By increasing the uncertainty in the position (blurr), the velocity uncertainty goes down, thus the kinetic energy will decrease. Therefore it desires the most uncertainty in position. The only thing preventing the electron to be a free particle is the attraction by the nucleus. It so to say limits the maximum uncertainty in position.

Classical orbits

Now you see, why we cannot speak of classical orbits anymore: because of uncertainty in both, position and velocity, we have to accept, that we just can track the electron down to a "cloud" around the nucleus with some speed.

I hope this explanation was clear in some sense. It has the price, to abandon things like orbits and to accept things like the uncertainty principle. But despite quantum mechanics beeing an overall "weird" theory (philosophically) at all, it explaines lots of things in our modern world and is considered to be the right theory for these applications.