In terms of quantum numbers, which has the highest value for the azimuthal quantum number for a given principal quantum number n?

The azimuthal quantum number, represented by the symbol 'l', describes the subshell or orbital shape within a given principal quantum level, indicated by the principal quantum number 'n'. The values of 'l' range from 0 to n-1 for each principal energy level.

For a specific principal quantum number 'n', the maximum value that 'l' can take is n-1. This is because:

• When n is 1, l can only be 0 (the s subshell).
• When n is 2, l can take the values 0 and 1 (the s and p subshells, respectively).
• When n is 3, l can take the values 0, 1, and 2 (the s, p, and d subshells).

Each increase in 'n' allows for one additional subshell, hence l can never equal 'n' itself, nor can it exceed that value. This makes n-1 the highest possible value for the azimuthal quantum number for a given principal quantum number 'n'.

Consequently, stating that the azimuthal quantum number has its highest value at n-1 accurately reflects the allowed quantum number values in the context of