Each atomic orbital has designated shapes that are determined by the **angular momentum quantum number (l)**.

Concept #1: Quantum Numbers and Atomic Orbital Shape

Example #1: Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:

a) n = 8, l = 1, m_{l} = 1/2

b) n = 8, l = 2, m_{l} = -2

c) n = 8, l = 0, m_{l} = 1

d) n = 8, l = 0, m_{l} = 0

Practice: Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:

a) n = 2, l = 1, ml = +1, ms = -1

b) n = 4, l = 1, ml = -2, ms = +1/2

c) n = 3, l = 1, ml = -1, ms = 0

d) n = 2, l = 1, ml = +1, ms = -1/2

Which of the following statements is TRUE?
a. Atoms are roughly spherical because when all of the different shaped orbitals are overlapped, they take on a spherical shape.
b. We can know the exact location and exact speed of an electron at the same time.
c. Since electrons have mass, we must always consider them to have particle properties and never wavelike properties.
d. All orbitals in a given atom are roughly the same size.
e. All of the above are true.

Which sketch represents an orbital with the quantum numbers n = 3, l = 0, and ml = 0?

The orbitals of 2p electrons are often represented as being
(A) elliptical
(B) dumbbell shaped
(C) tetrahedral
(D) spherical

Which quantum numbers below could correctly describe the orbital to the right?
(a) n = 1, l = 0, m l = 0
(b) n = 2, l = 2, m l = 1
(c) n = 3, l = 1, m l = -1
(d) n = 3, l = 2, m l = -3
(e) n = 3, l = 2, m l = 2

Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:
a) n = 2, ℓ = 1, m ℓ = 0
b) n = 3, ℓ = 2, m ℓ = –1
c) n = 4, ℓ = 0, m ℓ = +1
d) n = 1, ℓ = 1, m ℓ = 0

Based on the following atomic orbital shape, which of the following set of quantum numbers is correct:
a) n = 3, ℓ = 2, m ℓ = 0, m s = –1/2
b) n = 3, ℓ = 1, m ℓ = –3 , m s = 1
c) n = 4, ℓ = 0, m ℓ = 0, m s = –1/2
d) n = 4, ℓ = 2, m ℓ = –3, m s = –1/2

Which of the following illustrates an orbital with quantum numbers n = 5, l = 1?

Consider an atom of Zirconium (Zr) where the electrons are in the ground state. How many electrons would be in orbitals that are spherical in shape?
A. 2 B. 10 C. 17 D. 20 E. 25

Classify the following statements
as either true or false:In a contour representation of an orbital,
such as the one shown here for
a 2p orbital, the electron is confined to move about the nucleus
on the outer surface of the shape.

Sort sketches of the general shapes into the s, p and d orbitals.

Why are atoms usually portrayed as spheres when most orbitals are not spherically shaped?

Use the relative size of the 3s orbital represented below to answer the question.Which orbital has the highest value of n?a. Ab. Bc. Cd. D

Sketch the shape and orientation of the following types of orbitals: (a) s

Sketch the shape and orientation of the following types of orbitals: (b) p z

Sketch the shape and orientation of the following types of orbitals: (c) d xy

Sketch the shape and orientation of the following types of orbitals: (a) p x

Sketch the shape and orientation of the following types of orbitals: (b) d z2

Sketch the shape and orientation of the following types of orbitals: (c) d x2-y2

Use the relative size of the 3s orbital represented below to answer the following question.In an atom, how many other orbitals will have both a value of n and a shape identical to Orbital C? (Use Orbital C as a reference and do not include it in your count.)a. 1b. 2c. 3d. 4

Use the relative size of the 3s orbital represented below to answer the following question.Which orbital has the highest energy?a. Ab. Bc. Cd. D

A certain electron in an atom is in an orbital that has two lobes of electron density. Choose the orbital that matches this description.A. 3d B. 5s C. 4f D. 2p E. 6s

All of the following statements are true, EXCEPT:a. the n = 2 energy level has d orbitalsb. the 2p orbitals can have a max of 6 electronsc. the s orbital has a spherical shaped. there are 5 d orbitals in a sete. the fourth major energy level has one set of f orbitals.

All the following statements are true excepta) The n = 3 energy level has no f orbitalsb) The 2p orbitals can have a maximum of 6 electronsc) Each p orbital has a dumbbell shaped) There are 10 d orbitals in a sete) The fourth major energy level has one set of f orbitals

All the following are true EXCEPTa. the n = 3 shell has no f subshellb. there are three p orbitals in every shell of an atom except the n = 1 shellc. all s orbitals have spherical shapesd. each d subshell has five d orbitalse. the energies of subshell in the shells (energy levels) of a hydrogen atom vary as s < p < d, etc.

Which is NOT directly determined by the principal quantum number, n, of the electron hydrogen atom?(A) The energy of the electron(B) The minimum wavelength of the light needed to remove the electron from the atom(C) The size of the corresponding atomic orbital(s)(D) The shape of the corresponding atomic orbital(s)(E) All of the above

The s orbital is spherical (nondirectional) because:a. an s orbital has angular nodes.b. at a particular distance from the nucleus, the electron probability is the same in all directions.c. the angular wave function of an s orbital depends on the value of l.d. the angular wave function for all s orbitals is a constant.e. the angular wave function of an s orbital varies with the principal quantum number (n).f. the electron probability is zero at the nucleus.

In defining the sizes of orbitals, why must we use an arbitrary value, such as 90% of the probability of finding an electron in that region?

Sketch the boundary surface of a dx2−y2 and a py orbital. Be sure to show and label the axes.

Sketch the px and dxz orbitals. Be sure to show and label the coordinates.

Here are sketches of four electron orbitals: