$($a$)$ How many different sets of quantum numbers $($n$,$ l$,$ ml $,$ ms $)$ are possible for an electron

in the $5$f level?

$($b$)$ Suppose a certain atom has three electrons in the $3$d level. What is the maximum

possible value of the total ms of the three electrons?

$($c$)$ What is the maximum possible total ml of three $3$d electrons? Assume an external

magnetic field along the Z$-$axis splits the state, and apply the Aufbau principle. Total ml $=$

sum of all $($ml $).$ There are two possible answers that I can think of$.$

$($d$)$ Suppose an atom has ten electrons in the $5$f level. What is the maximum possible value

of the total ms of the ten $5$f electrons?

e$)$ What is the maximum possible total ml of ten $5$f electrons?