Which quantum number has only two possible values?
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Answers
Answer:
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Answer:
The spin quantum number has only two possible values of +1/2 or -1/2. If a beam of hydrogen atoms in their ground state (n = 1, ℓ = 0, mℓ = 0) or 1s is sent through a region with a spatially varying magnetic field, then the beam splits into two beams.
SternGerlachSternGerlach
Clearly the three quantum numbers, n, ℓ, mℓ, are not enough to completely describe the state of the H-atom, Another quantum number is required to describe whether it goes up or down in a spatially varying magnetic field. This property is called spin because if electrons were balls of charge spinning about their own axes, they would behave in this way in a magnetic field. Actually, this is not a correct picture. The spin quantum number shows up when the wave function of quantum mechanics is modified to include the effects of relativity.
The electron spin is very important in understanding the electronic structure of atoms containing many electrons (not just one like Hydrogen) because of the Pauli Exclusion Principle.
Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers n, ℓ, mℓ, ms.
Since there are only two values of ms, then any orbital can only hold two electrons with opposite vales of ms. Any more would violate Pauli's Principle.
In summary, you can think of electron orbitals as standing waves of the electron wave function when it is bound to a postively charged nucleus. Remember, however, that the electron is not just a wave. It is a particle with wave-like properties. The wave function squared gives the probability of finding the electron at any particular position.
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