Question

In an atom, what is the maximum number of electrons that can have the following quantum numbers?

(a) n = 3, ms = +1/2

(b) n = 6, l = 2

(c) n = 3, l = 2, ml = -1

(d) n = 4, l = 3, ml = +1

Answer 1

n = 3, ms = +1/2

the rule

# electrons = 2n^2

then

for

n = 3; ... 2*(3)^2 = 18 electrons, but is Ms = +1/2; only one half is possible, then 9 electrons

b)

for n = 6

n = 2*(6^2) = 72 electrons

for l = 2; then we have,

ml = 0,+/- 1 and +/- 2; each one of them has 2 electorns, then 2+2+2 = 6 electrons are possible

c)

if ml = -1

then

it can only have +1/2 and -1/2 electrons in spin, therefore, only 2 electrons is the answer

d)

same as in c

ml = +1

then the +/- 1/2 will be the answer o 2 electrons