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This question already has an answer here:

I want to know that how an electron is in continuous motion.

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marked as duplicate by Chris, Kyle Kanos, Jon Custer, stafusa, Phonon Jan 31 '18 at 22:37

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  • $\begingroup$ If you swing a rock around on a string, the centripetal & centrifugal forces on it are equal. If they were not, the rock would either fly away or crash to the centre. The same goes for a planet and satellite, and the electron/nucleus. Except that the electron does not really fly around the nucleus. $\endgroup$ – hdhondt Jan 31 '18 at 6:14
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    $\begingroup$ Also, remember that the centrifugal force does not exist in reality. It is just the feeling of being swung out of the circle. It is no force. So there is only the centripetal force acting as the net force inwards on the circle. $\endgroup$ – Steeven Jan 31 '18 at 6:51
  • $\begingroup$ @Steeven: You are wrong xkcd.com/123 $\endgroup$ – CriglCragl Jan 31 '18 at 10:32
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    $\begingroup$ Possible duplicate of Why don't electrons crash into the nuclei they "orbit"? $\endgroup$ – Kyle Kanos Jan 31 '18 at 11:04
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Let's leave electrons aside because they're not classical objects - one can't even safely say that the electrons are revolving around the nucleus. There's a definite orbital they're in according to quantum mechanics, but the position of the electron is never completely specified and not always a certain distance from the nucleus. Instead we'll use a person swinging a ball.

The simple answer to your question is that there's no centrifugal force. You're right that if there were centrifugal force and it's of equal strength to centripetal force, then the ball would simply move in a straight line. Here's what all the forces are:

For the person: he must apply a force to keep the ball revolving. The outward force he feels is the reaction of the force he must apply (by Newton's 3rd law).

For the ball: the ball only feels the centripetal force (and gravity but we neglect that).

For an observer on the ball: for the observer to stay put on the ball, he must also feel the centripetal force. This can be transferred from the ball to him by a variety of ways, e.g. friction, if the observer is grabbing hold of the ball, and so on. In all cases the observer doesn't actually feel a "centrifugal force" - he's just feeling the force needed to keep him revolving. If he lets go of the ball then he'll fly off the ball and move in a straight line; he won't suddenly fly outwards as a centrifugal force implies.

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If you observe an electron from outside the atom (in the rest frame of the atom) you "see" the electron orbiting the nucleus under the influence of the attractive electrostatic force between the negative electron and the positive nucleus.
This attractive electrostatic force, the only force acting on the electron, produces a centripetal acceleration of the electron causing it to orbit the nucleus.

If you "sit" on the electron (observe the electron in the rest frame of the electron) you do not see the electron moving or accelerating relative to you.
However the electron does feel the attractive electrostatic force between the negative electron and the positive nucleus.
To reconcile the fact that there is an attractive electrostatic force on the electron and yet it is not accelerating relative to you another force is introduced which is equal in magnitude and opposite in direction to the attractive electrostatic force between the negative electron and the positive nucleus and this force is called a centrifugal force.
So as far as you are concerned "sitting" on the electron (being in the rest frame of the electron) the net force on the electron is zero and it is not accelerating relative to you.
With the introduction of the centrifugal force Newton's second law works in the frame of reference of the electron.

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Yes, magnitude wise these two are equal but they both appear in different reference frames. If we are observing an electron revolving around the nucleus then we would say that it is under centripetal force which keeps it in circular motion but if we were in the frame of nucleus then we would use centrifugal force to define the circular motion of it.

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The electrostatic attraction is balanced by the https://en.m.wikipedia.org/wiki/Exchange_interaction The wavefunction of the electron has a probability distribution for measurements of position and velocity, which is not the same as continuous orbital motion, even though it is the quantum analogue.

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