The principal quantum number, n, has values n = 1,2,3,4,5...
The orbital angular momentum (azimuthal) quantum number, l, has values l = 0,1,2,3 .... (n-1)
The magnetic quantum number, ml, has values ranging from negative l to positive l including zero. The total number of states is (2l + 1)
The spin quantum number has two possible values only (-1/2 and +1/2)
(a) How many different values of l are possible for an electron with principal quantum number n = 4?
(b) How many values of ml are possible for an electron with orbital quantum number l = 4?
(c) The quantum state of a particle can be specified by giving a complete set of quantum numbers (n, l, ml, ms). How many different quantum states are possible if the principal quantum number is n = 2?
To find the total number of allowed states, first write down the allowed orbital quantum numbers l, and then write down the number of allowed values of ml for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin.
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