what is spin quantum number. what information we get from it
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The Spin Quantum Number ( ms ) describes the angular momentum of an electron. An electron spins around an axis and has both angular momentum and orbital angular momentum. Because angular momentum is a vector, the Spin Quantum Number (s) has both a magnitude (1/2) and direction (+ or -).
Each orbital can only hold two electrons. One electron will have a +1/2 spin and the other will have a -1/2 spin. Electrons like to fill orbitals before they start to pair up. Therefore the first electron in an orbital will have a spin of +1/2. After all the orbitals are half filled, the electrons start to pair up. This second electron in the orbital will have a spin of -1/2. If there are two electrons in the same orbital, it will spin in opposite directions.
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Each orbital can only hold two electrons. One electron will have a +1/2 spin and the other will have a -1/2 spin. Electrons like to fill orbitals before they start to pair up. Therefore the first electron in an orbital will have a spin of +1/2. After all the orbitals are half filled, the electrons start to pair up. This second electron in the orbital will have a spin of -1/2. If there are two electrons in the same orbital, it will spin in opposite directions.
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In atomic physics, the spin quantum number is a quantum number that parameterizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle.
So it is a function of 3 quantum numbers: n, l, and ml. it turns out that n and l are actually summation indices that tell you how many terms in the polynomial to include, which is why they can only be non zero positive integers (it also turns out l has to be less than n). ml on the other hand is the argument of a trig function and you should note that cos(1*Pi) = cos(2*pi) =c os(-1*pi), etc. This is why ml can be any integer positive or negative ( but it is still bound by the values of n and l). I left the spin quantum number out of this because it doesn't actually appear in the solution to the standard Schrodinger equation for the hydrogen atom, it is just usually tac'd on at the end like it does (you need to invoke some relativity to get the spin quantum number out).
This example was just for the hydrogen atom, but this happens for all bound quantum system. Although, all system will not have the amount of quantum numbers and those numbers may qualitatively represent different things. As has already been said, in hydrogen they are associated with the total energy (n), the angular momentum (l) and the magnetic moment (ml).
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So it is a function of 3 quantum numbers: n, l, and ml. it turns out that n and l are actually summation indices that tell you how many terms in the polynomial to include, which is why they can only be non zero positive integers (it also turns out l has to be less than n). ml on the other hand is the argument of a trig function and you should note that cos(1*Pi) = cos(2*pi) =c os(-1*pi), etc. This is why ml can be any integer positive or negative ( but it is still bound by the values of n and l). I left the spin quantum number out of this because it doesn't actually appear in the solution to the standard Schrodinger equation for the hydrogen atom, it is just usually tac'd on at the end like it does (you need to invoke some relativity to get the spin quantum number out).
This example was just for the hydrogen atom, but this happens for all bound quantum system. Although, all system will not have the amount of quantum numbers and those numbers may qualitatively represent different things. As has already been said, in hydrogen they are associated with the total energy (n), the angular momentum (l) and the magnetic moment (ml).
HOPE MY ANEWER HELPS YOU
@adityaprakash0574
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