7.3.2 Atomic Orbital Shapes and Quantum Numbers

Question 1

Atomic Orbital Shapes and Quantum Numbers

Answer 1

• According to the Schrödinger equation, there are three quantum numbers: n, l, and m l .
• The value of l determines the shape of the orbital.

Question 2

note

Answer 2

• According to the Schrödinger equation, there are three
  quantum numbers: n, l, and m l .
• The principal quantum number (n) is a positive integer
  describing the energy level of the electron.
• The angular momentum quantum number (l) can be an
  integer from 0 to n – 1, and describes the shape of the orbital.
• The magnetic quantum number (m l ) can be an integer from –l to +l, and describes the orientation of the orbital.
• The value of l is equal to the number of angular nodes, and therefore determines the shape of the orbital.
• Orbitals with l = 0 have zero angular nodes, and are therefore spherical. Orbitals with l = 0 are s orbitals.
• Orbitals with l = 1 have one angular node, and are therefore dumb-bell shaped. Orbitals with l = 1 are p orbitals.
• Orbitals with l = 2 have two angular nodes, and are cloverleaf shaped or described by a nodal cone. Orbitals with l = 2 are d orbitals.
• Orbitals with l = 3 have three angular nodes, and have
  complex shapes. Orbitals with l = 3 are f orbitals.

Question 3

What are the values for ml for a d orbital?

Answer 3

−2, −1, 0, 1, 2

Question 4

What are the permissible values for the angular quantum number (l) when n = 3?

Answer 4

0, 1, 2

Question 5

There are three p orbitals that are aligned with their major axes along the x, y, and z axes, what is the origin of these three p orbitals?

Answer 5

They are the solutions for the three values of the magnetic quantum number.

Question 6

What are the permissible values for the angular quantum number (l) when n = 2?

Answer 6

0, 1

Question 7

What are the values for ml  for a p orbital?

Answer 7

−1, 0, 1

Question 8

What is the difference between a 2p and a 3p orbital.

Answer 8

The 3p orbital is farther from the nucleus than the 2p orbital.

Question 9

What are the permissible values for the angular quantum number (l) when n = 4?

Answer 9

0, 1, 2, 3

Question 10

How many angular nodes do the d orbitals have?

Answer 10

2

Question 11

What is an orbital?

Answer 11

The probability of finding an electron in a region.

Question 12

What are the names for the three quantum numbers in the Schrödinger equation?

Answer 12

Principal, angular, magnetic.