In quantum mechanics, what is the largest value of the angular momentum quantum number (l) possible for a principal quantum number (n) of 5?

In quantum mechanics, the angular momentum quantum number, denoted as ( l ), determines the shape of an electron's orbital. Its value is dependent on the principal quantum number, ( n ), which indicates the energy level of an electron in an atom.

The relationship between the principal quantum number and the angular momentum quantum number is that ( l ) can take on integer values starting from 0 up to ( n - 1 ). Therefore, for any given ( n ), the possible values of ( l ) are:

[ l = 0, 1, 2, ..., (n - 1) ]

For a principal quantum number of ( n = 5 ), the highest allowable value for ( l ) would be ( n - 1 ), which is:

[ l = n - 1 = 5 - 1 = 4 ]

This means that the largest value for the angular momentum quantum number when ( n ) is 5 is 4. Thus, the answer indicating that the largest value of ( l ) is 4 accurately reflects the fundamental rules governing quantum states and their respective quantum numbers.