Question

In the ground state of element 115, Uup,
a. how many electrons have n = 5 as one of their quantum numbers?
b. how many electrons have l = 3 as one of their quantum numbers?
c. how many electrons have ml = +1 as one of their quantum numbers?
d. how many electrons have ms = -1/2 as one of their quantum numbers?

Answer 1

In the ground state of element 115, Uup, the electronic configuration is written as:

[Rn] 5f 14 6d 10

a. Since 5s, 5p,5d and 5f all are completely filled hence 2+6+10+14=32 electrons have n = 5 as one of their quantum numbers.

b. f subshell has azimuthal quantum number (l) =3, total no. of electrons in f Subshell= 4f+5f= 14+14=28 electrons

c. ml= +1 is present in p, d, f subshells

2p,3p,3d,4p,4d,4f,5p,5d,5f = 9(2)= 18 electrons

d. Electrons present in each orbital should have different spin (Hund's rule).

Total electrons = 115,so 57 electrons have -1/2 spin while 58 have +1/2 spin.