Atomic Orbital Shapes and Quantum Numbers (7.3.2)

Question 1

• According to the Schrödinger equation, there are three quantum numbers: n, l, and m l.

Answer 1

• According to the Schrödinger equation, there are three quantum numbers: n, l, and m l.

Question 2

• The value of l determines the shape of the orbital.

Answer 2

• The value of l determines the shape of the orbital.

Question 3

According to the Schrödinger equation, there are
three quantum numbers: n, l, and ml. 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 (ml) 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.

Answer 3

According to the Schrödinger equation, there are
three quantum numbers: n, l, and ml. 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 (ml) 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 4

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

Answer 4

0, 1, 2, 3 (C)

Question 5

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

Answer 5

Principal, angular, magnetic. (D)

Question 6

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 6

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

Question 7

What are the values for m l for a d orbital?

Answer 7

−2, −1, 0, 1, 2 (D)

Question 8

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

Answer 8

0, 1 (D)

Question 9

What is an orbital?

Answer 9

The probability of finding an electron in a region. (A)

Question 10

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

Answer 10

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

Question 11

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

Answer 11

0, 1, 2 (B)

Question 12

What are the values for m l  for a p orbital?

Answer 12

−1, 0, 1 (C)

Question 13

How many angular nodes do the d orbitals have?

Answer 13

2 (C)

The d orbitals have a numerical value of 2 and have 2 angular nodes, either two nodal planes or nodal cones.