Question

Orbitals and Quantum Numbers

Each atomic orbital is specified by a unique set of n, l and ml quantum numbers:

1a. What quantum number/s do the two spherical orbitals have in common? What quantum number/s would be different? Are these orbitals s, p or d?

1b. Write down a possible set (n, l, ml) of quantum numbers for each spherical orbital.

1c. Consider the dumb-bell shaped orbitals. What quantum number/s do these three orbitals have in common? What quantum number/s would be different? Are these s, p or d orbitals?

1d. Write down a possible set of quantum numbers for each dumb-bell shaped orbital

1e. What quantum number/s do the 4-leaf clover-shaped orbitals share? Are these s, p or d orbitals? Rules of quantum numbers:

2a. Complete the table below: if there is more than one possibility for an answer, use ‘OR’ to indicate the other possibilities.

Orbital Label	n	l	ml
5s
4d	4	2
	2	1	0
	2	1	-1

2b. How many orbitals are possible for the n = 3 level? List all the orbitals and their quantum numbers.

2c. Which of the following sets of quantum numbers is NOT allowed by the rules? (there may be more than one answer) Why?

n = 3, l = -2, ml = 0
n = 4, l = 4, ml = 2
n = 3, l = 2, ml = 3
n = 3, l = 1, ml = -1
n = 0, l = 1, ml = 0

2d. Which of the following orbital designations is incorrect and why?

i. 3s
ii. 1p
iii. 6s
iv. 4f
v. 2d

Answer 1

la. Spherical orbital: S-orbital Number) angular quantum number = 0 & magnetic Q. M is also (common quantur cane and o Two quantum numbers are same: one is different (n). 16. na 1,2,3,4.. ero meo (C . same &Q. No = e different a, No. an, m dum b-bell shaped arbital - prosbital n=2, 3, 4, ... , 1=1, marl or o ogle Id. le. four - leaf clover. shaped arbital = doorbital. doublea dumb.bell shape 2a. n=5 n=u l=0 l=2 mo m=-2,-1,0,1,2 n=2 2P2 2Pxq2ly n=3 mzo mand n=2 t=1 ab. la l=2 m=~2,-1,0, 1, 2 mzo maryo Total g-gbitals. ac (b) n = 4, 1=4, m=2 not allowed (c) n= 3,1=2, mas not allowed (@) nao, dal, mão not allowed ad, Ip and ad (kn) (m. (m (1¢n) nal, l=1 not possibe. na 2,222 not possible.