Question

Each electron in an atom may be described by a set of four quantum numbers. For each of the following, write down each different set of quantum numbers possible such that each set contains the given value. (The answer for part (a) has been done for you below.) a. n = 3, l = 1 b. n = 3, l = 2 c. n = 4, l = 2 d. n = 3, l = 2, ml = –2 e. n = 3, l = 0, ml = 0 Could you guide me through how to solve this problem?

Answer 1

l value sublevel

0 s

1 p

2 d

ml values

ml values for s-sublevel is 0. ( s sublevel has 1 orbital)

ml values for p-sublevel are -1,0,+1 ( p sublevel has 3 orbitals)

ml values for d-sublevel are -2,-1,0,+1,+2 ( d sublevel has 5 orbitals)

a) n = 3, l = 1

  n = 3, l = 1 , ml =  -1,0,+1 , s = +1/2, -1/2

Therefore, possible sets are

n = 3, l = 1 , ml =  -1 s = +1/2 or -1/2

n = 3, l = 1 ml = 0 s = +1/2 or -1/2

n = 3, l = 1 ml = +1 , s = +1/2 or -1/2

b)  n = 3, l = 2

n = 3, l = 2 , ml = -2,-1,0,+1,+2 , s = +1/2, -1/2

Therefore, possible sets are

n = 3, l = 2 , ml =  -2 s = +1/2 or -1/2

n = 3, l = 2 , ml =  -1 s = +1/2 or -1/2

n = 3, l = 2 ml = 0 s = +1/2 or -1/2

n = 3, l = 2 ml = +1 , s = +1/2 or -1/2

n = 3, l = 2 , ml = +2 s = +1/2 or -1/2

c) n = 4, l = 2

n = 4, l = 2 , ml = -2,-1,0,+1,+2 , s = +1/2, -1/2

Therefore, possible sets are

n = 4, l = 2 , ml =  -2 s = +1/2 or -1/2

n = 4, l = 2 , ml =  -1 s = +1/2 or -1/2

n = 4, l = 2 ml = 0 s = +1/2 or -1/2

n = 4, l = 2 ml = +1 , s = +1/2 or -1/2

n = 4, l = 2 , ml = +2 s = +1/2 or -1/2

d) n = 3, l = 2, ml = –2

n = 3, l = 2, ml = –2 , s = +1/2 or -1/2

e) n = 3, l = 0, ml = 0

n = 3, l = 0, ml = 0,  s = +1/2 or -1/2