how is it that:electrons near the nucleus have greater potential energy and away from it have less potential energy?

Dear saikat,

Electrons moving in circular orbits at constant speed around a nucleus, which is actually an approximation of reality, are said to exhibit periodic motion. This is the same motion exhibited by a mass attached to a spring, a pendulum, or the motion of small segments of a violin string when it is bowed. To see this, let's look at our first demonstration, which compares motion about a circle to a standing wave on a string.

Figure: a) body moving a constant speed (NOT velocity) around a circle

b) motion viewed edge-on; c) motion of a segment of a standing wave on a rope (lower right).

Let's compare the motion of the body moving around the circle to that of a segment of a stretched rope undergoing oscillation. One can see (Figure 4) that the motion of the body, when viewed edge on, is identical to that of a segment of the oscillating rope.

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Sagar Singh

B.Tech IIT Delhi