Why are only certain electron wave modes allowed in the vicinity of the nucleus?

Question

Why are only certain electron wave modes allowed in the vicinity of the nucleus? What is the criterion for being allowed?

The wave function must interfere constructively on many oscillations.

The wave function must interfere destructively on many oscillations.

There must be only one wave around the nucleus.

Each electron must have a different wave function from all the others.

The wave function must interfere constructively on many oscillations.

The wave function must interfere destructively on many oscillations.

There must be only one wave around the nucleus.

Each electron must have a different wave function from all the others.

Explanation / Answer

here ,

only certain electron wave modes allowed in the vicinity of the nucleus.it is same as the musical instruments .It is well known that musical instruments operate by the principle of resonance. That is, they are so constructed that only certain sounds can be made by them. Sounds are waves and, as such, can be mathematically described by their size (loudness) and their frequency (pitch). Musical instruments will only make certain frequencies and combinations of frequencies. same goes for electrons in an atom.

hence , the correct choice is

a.   The wave function must interfere constructively on many oscillations.

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