9. Quantum Mechanics

The contour representat ion z of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (a) What is the quantum number l for this orbital?

The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (b) What is the value of the angular momentum quantum number, l?

Identify each of the following orbitals, and give n and l quantum numbers for each. (a)

(b)

(a) For n = 4, what are the possible values of l?

Give the numerical values of n and l corresponding to each of the following orbital designations: (d) 5d.

Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p.

What are the possible values of l for each given value of n? a. 1 b. 2 c. 3 d. 4

Which of the following represent impossible combinations of n and l? (a) 1p (b) 4s (c) 5f (d) 2d

Which combinations of n and l represent real orbitals, and which do not exist? a. 1s b. 2p c. 4s d. 2d

Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

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

Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?

(a) The average distance from the nucleus of a 3s electron in a chlorine atom is smaller than that for a 3p electron. In light of this fact, which orbital is higher in energy?

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this imaginary universe and ours, how many orbitals would exist in each level? a. n = 1 b. n = 2 c. n = 3

What do the different colors in the two lobes of the p orbitals specify?

What is the l quantum of an orbital that has four lobes that resemble a cloverleaf?

Imagine a universe in which the four quantum numbers can have the same possible values as in our universe except that the angular-momentum quantum number l can have integral values of 0, 1, 2...n + 1 (instead of 0, 1, 2..., n - 1). (a) How many elements would be in the first two rows of the periodic table in this universe?

What quantum numbers specify these subshells?

Which subshell (for example, 1𝑠 ) is designated by each set of quantum numbers?