The electrons do not fall into the nucleus because they have a velocity that keeps them in orbit. The attraction between the positive and negative charges is enough to continually turn the electrons so that the move in a circle, but it is not strong enough to get them any closer to the nucleus.

If the electrons had no velocity, they would fall right into the nucleus. The same could be said of the moon and the earth or the earth and the sun. If the moon had no velocity of its own, it would crash into the earth since the earth’s gravity attracts the moon to it. In the same way, if the earth did not have velocity, the sun would pull it right in. However, since the earth has its own velocity, the sun cannot pull it in. Instead, it can only turn it to make it move in (almost) a circle. In the same way, the moon does not crash into the earth because of its velocity and the electrons do not crash into the nucleus.

When you did Experiment 11.1, you experienced this same effect. By twirling the weight, you gave it its own velocity. The string, however, was pulling the weight into the center of the circle. The weight never got to the center, however, because the string’s force (the centripetal force) was not great enough to pull the weight in. The best it could accomplish was to continually turn the weight so that it moved in the circle.

The centripetal force of the electrical attraction between electrons and protons is strong enough to keep the electrons turning, but not strong enough to pull them in.