Question

How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.

Short answer

Electrons and planets orbit around atom and sun respectively, but electrons can change orbits whereas for planet one orbit is fixed and continuous. The correspondence is that atom and sun is heavier than electrons and planets respectively and they exert gravity force and coulomb force respectively.

Step-by-step solution

Determine correspondence principle 

The correspondence principle says that in the limit of high quantum numbers, the behaviour of systems represented by quantum mechanics (or by the old quantum theory) reproduces classical physics.

Orbits and Electrons

Allowed orbits for electrons are discrete or quantized, meaning that only certain orbits are allowed. Each orbit has a different energy,and electrons can move to other orbits by emitting or absorbing energy, which is also quantized.On the other hand, planets can have any orbit given the right amount energy or, in other words,allowed orbits for planets are continuous.

Determine conclusion by correspondence principle

The correspondence here is the fact thatboth planets and electrons orbit around a large-mass body comparedfor planets that force is gravity, and for electrons it's the attractive Coulomb force.

Therefore, orbits of atoms and planets differ and the correspondence principle is applied on both.