Quantum Numbers and Orbitals

Quantum Numbers and Orbitals

1. Quantum Number Values

a. For n = 3, the values of the magnetic quantum number (m) for different angular momentum quantum numbers (l) are:

• When l = 0 (s orbital), m = 0
• When l = 1 (p orbital), m = -1, 0, +1
• When l = 2 (d orbital), m = -2, -1, 0, +1, +2

b. When n = 3, i.e., for different l:

• For l = 0: m = 0
• For l = 1: m = -1, 0, +1
• For l = 2: m = -2, -1, 0, +1, +2

c. For n = 3, when l = 2 :

• m can take values -2, -1, 0, +1, +2

d. For n=5, the values of m based on l are:

• When l = 0 (s orbital), m = 0
• When l = 1 (p orbital), m = -1, 0, +1
• When l = 2 (d orbital), m = -2, -1, 0, +1, +2
• When l = 3 (f orbital), m = -3, -2, -1, 0, +1, +2, +3

2. Orbital Quantum Numbers

a. 1s

• Principal quantum number (n): 1
• Angular momentum quantum number (l): 0

b. 3s

• Principal quantum number (n): 3
• Angular momentum quantum number (l): 0

c. 2p

• Principal quantum number (n): 2
• Angular momentum quantum number (l): 1

d. 4d

• Principal quantum number (n): 4
• Angular momentum quantum number (l): 2

e. 5f

• Principal quantum number (n): 5
• Angular momentum quantum number (l): 3

3. Possible m Values for Orbitals

a. s Orbital

• Angular momentum quantum number (l) is 0, so possible m values: 0

b. p Orbital

• Angular momentum quantum number (l) is 1, so possible m values: -1, 0, +1

c. d Orbital

• Angular momentum quantum number (l) is 2, so possible m values: -2, -1, 0, +1, +2

d. f Orbital

• Angular momentum quantum number (l) is 3, so possible m values: -3, -2, -1, 0, +1, +2, +3

4. Possible Orbitals for n = ?

• The total number of orbitals available is given by the formula:
  $2l + 1$ where l ranges from 0 to n-1.
• For each value of n, the number of orbitals is equal to:
  • When n = 1: 1 orbital (l = 0)
  • When n = 2: 4 orbitals (l = 0 and l = 1)
  • When n = 3: 9 orbitals (l = 0, 1, and 2)
  • When n = 4: 16 orbitals (l = 0, 1, 2, and 3)
  • When n = n: $n^2$ possible orbitals.