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Mathematics, 30.11.2019 03:31 cahree
Learning goal: to learn the restrictions on each quantum number. quantum numbers can be thought of as labels for an electron. every electron in an atom has a unique set of four quantum numbers. the principal quantum number n corresponds to the shell in which the electron is located. thus n can therefore be any integer. for example, an electron in the 2p subshell has a principal quantum number of n=2 because 2p is in the second shell. the azimuthal or angular momentum quantum number ℓ corresponds to the subshell in which the electron is located. s subshells are coded as 0, p subshells as 1, d as 2, and f as 3. for example, an electron in the 2p subshell has ℓ=1. as a rule, ℓ can have integer values ranging from 0 to n−1. the magnetic quantum number mℓ corresponds to the orbital in which the electron is located. instead of 2px, 2py, and 2pz, the three 2p orbitals can be labeled −1, 0, and 1, but not necessarily respectively. as a rule, mℓ can have integer values ranging from −ℓ to +ℓ. the spin quantum number ms corresponds to the spin of the electron in the orbital. a value of 1/2 means an "up" spin, whereas −1/2 means a "down" spin.
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