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, m_{l}, 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 *m*_{l} 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*, *m** _{l}*,

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 *m*_{l} 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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