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In theory, the number of electrons with each quantum number is not limited. However, for any given "main quantum number" (n), the number of electrons having the other quantum numbers is limited - but it depends on the value of "n". For more information, the Wikipedia article on "quantum number" seems to give a good overview.
The spin quantum number was created in the early twentieth century to account for the magnetic properties of the electron. It has only two possible values, +1/2 and -1/2, which indicates the two possible spin states of the electron. A single orbital can hold up to 2 electrons, which must have opposite spin states.
For each level (main quantum number) number "n", there are 2 times n squared electrons. The reasons are related to the Pauli Exclusion Principle, meaning that no two electrons can have the same values for all four quantum numbers.
Possible values of quantum numbers in order of n,l,m,s in the second shell:2,0,0,-1/22,0,0,+1/22,1,-1,-1/22,1,-1,+1/22,1,0,-1/22,1,0,+1/22,1,1,-1/22,1,1,+1/2
The bottom-line answer is because that is how nature works! However, there are somewhat less profound explanations, but they are really just rules which say that this must happen -- and don't ultimately answer "Why?". The Pauli Exclusion Principle says that all electrons in an atom must have four unique quantum numbers -- no two can have all four the same. This rule forbids more than 2 electrons existing in the same orbital because there are two possible quantum numbers available for that orbital -- electron spin of +1/2 and -1/2. But again, this rule just says that there can't be more than 2 electrons per orbital because of the uniqueness of quantum numbers -- but it doesn't say why quantum numbers must be unique! In the end, it really just is the way it because that's the way it is!
There can be two electrons with those quantum numbers in an atom. Each electron is completely described by four quantum numbers. The one that's missing in the list provided is ms, which can have only two possible values (+1/2 and -1/2).
In theory, the number of electrons with each quantum number is not limited. However, for any given "main quantum number" (n), the number of electrons having the other quantum numbers is limited - but it depends on the value of "n". For more information, the Wikipedia article on "quantum number" seems to give a good overview.
the spin quantum number has only two possible values__(+ 1/2 & -1/2)
Just two, +1/2, -1/2. These correspond to electrons of opposite spin.
For each level (main quantum number) number "n", there are 2 times n squared electrons. The reasons are related to the Pauli Exclusion Principle, meaning that no two electrons can have the same values for all four quantum numbers.
The spin quantum number was created in the early twentieth century to account for the magnetic properties of the electron. It has only two possible values, +1/2 and -1/2, which indicates the two possible spin states of the electron. A single orbital can hold up to 2 electrons, which must have opposite spin states.
For each level (main quantum number) number "n", there are 2 times n squared electrons. The reasons are related to the Pauli Exclusion Principle, meaning that no two electrons can have the same values for all four quantum numbers.
Possible values of quantum numbers in order of n,l,m,s in the second shell:2,0,0,-1/22,0,0,+1/22,1,-1,-1/22,1,-1,+1/22,1,0,-1/22,1,0,+1/22,1,1,-1/22,1,1,+1/2
10 electrons.The angular momentum quantum number is l (small L). This quantum number is dependant on the principal quantum number, and has values, 0 1,2 ..(n-1), where each value of n refers to a subshell known to chemists as followsn= 0, s orbital; n=1, p orbital; n= 2, d orbital; n= 3, f orbital.So we are looking at the d orbitals.There are five d orbitals, with magnetic quantum numbers running from -l to +l, that is -2, -1, 0, +1, +2Each of these can hold 2 electrons (with spin quantum numbers -1/2, +1/2)So we have 10 electrons that can have pricipal quantum numbers of 4 and angular monmentum quantum number of 2.
There isn't really some easy-to-understand explanation for why electrons behave like this, they just do.Electrons are fermions, and the definition of fermions includes the fact that no two of them in the same atom can have the same four quantum numbers. A "subshell" is defined by three quantum numbers, leaving only the fourth (spin) for them to be in different quantum states, and there are only two possible values for the spin quantum number, so there can only ever be two electrons in any given subshell.(Like a lot of things in science, it turns out that this is really lies-to-children; you can force electrons into the same quantum state if you overcome what's called electron degeneracy pressure, but it takes a LOT of force to do this, so unless you're actually inside a neutron star, assume that the electrons around you are following the Pauli exclusion principle.)
No. Electrons are fermions, meaning they cannot share the same set of four quantum numbers. Usually when we say "orbital" we only mean the first three, so there is room for two electrons in an orbital (corresponding to the two possible ms values).
The atomic states with principal quantum number 4 can have orbital angular momentum quantum numbers from -4 to 4. Hence there are 9 possible values of the orbital angular momentum quantum number. Each electron can have spin +1/2 or -1/2, so each of the states specified by a given orbital angular momentum quantum number can have at most two electrons in the state without violating Pauli's exclusion principle. So, in sum, there are 18 possible states for an electron with principal quantum number 4.