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## Example Questions

### Example Question #1 : Quantum Numbers

In terms of the principal quantum number, , how many electrons can be accommodated in a given energy level?

**Possible Answers:**

**Correct answer:**

For any n, the energy level can hold 2n^{2} electrons, since there are two electrons for each orbital.

### Example Question #2 : Quantum Numbers

What does the azimuthal quantum number reveal about the quantum mechanical model of an atom?

**Possible Answers:**

**Correct answer:**The shape and number of subshells within the energy level

The azimuthal quantum number is the second quantum number, designated by the letter l. It gives the shape and number of subshells in a principal energy level (shell).

### Example Question #3 : Quantum Numbers

Which of the following set of quantum numbers are not allowed: (a) n = 3, l = 2, ml = 0

(b) n = 2, l = 4, ml = –1 (c) n = 2.5, l = 1, ml = –1?

**Possible Answers:**

(a), (b)

(b), (c)

(a)

(a), (b), (c)

(c)

**Correct answer:**

(b), (c)

The sets of quantum numbers needs to follow the following rules: n (principal quantum

number) needs to be a positive integer, l can have any integral value from 0 to n – 1, and ml can range from –l to l. The only quantum numbers that follows these rules are (a).

### Example Question #4 : Quantum Numbers

How does energy vary as the quantum number (n) of an orbital changes?

**Possible Answers:**

As n increases, energy decreases

n is always constant, making the energy constant

As n increases, the energy increases as well

n has no effect on energy

**Correct answer:**

As n increases, the energy increases as well

The energy of an electron is related to the quantum number by the equation E = -R/n^{2}, where R is constant. The negative charge make it so that as n increases, the numerical value of the energy becomes less negative, approaching zero. Thus the energy increases as n increases.

### Example Question #4 : Quantum Numbers

What is the angular momentum quantum number for the highest energy orbital in the ground state Manganese atom?

**Possible Answers:**

1

0

None of the other answers

3

2

**Correct answer:**

2

First, we will write out the electron configuration for the ground state Manganese atom, considering only the valence electrons:

The orbitals highest in energy will be filled last, so our highest energy orbitals are orbitals.

The angular momentum quantum number describes the shape of the orbital, with orbitals corresponding to , orbitals corresponding with , and orbitals corresponding to , and so on.

We are considering a orbital, so .

### Example Question #5 : Quantum Numbers

Which of the following sets of quantum numbers could never be used to describe an electron?

**Possible Answers:**

**Correct answer:**

The principle quantum number, , must always be an integer greater than zero.

The angular momentum quantum number, , can have values from zero up to .

The magnetic quantum number, , ranges from to .

The spin quantum number, , must be or .

To total, a set of quantum numbers follows the pattern:

The only answer option that presents an invalid set of quantum numbers is . In this option, the angular momentum quantum number, , has an illegal value; it must be between zero and , and thus cannot be equal to 3.

### Example Question #6 : Quantum Numbers

Which set of quantum numbers represents the highest energy valence electron in a ground-state aluminum atom?

**Possible Answers:**

**Correct answer:**

The aluminum atom has its furthest electrons in the *3p* shell. We know this because aluminum is in the third row of the periodic table, and is in the p-block. The possible quantum numbers for any valence electron are:

### Example Question #7 : Quantum Numbers

Which of the quantum number describes the shape of the orbital where an electron is located?

**Possible Answers:**

*l*

*m _{s}*

*m _{l}*

*n*

**Correct answer:**

*n*

There are four quantum numbers; *l* indicates the type of orbital (*s, p, d, f*), which describe the shape of the orbital. An *s *orbital is spherical, *p* orbitals are dumbbell shaped, *d* and *f* orbitals are slightly more elongated than *p* orbitals. The *n *quantum number denotes the energy level, and can be positive integers only. The magnetic quantum number, *m _{l}*

_{ }denotes the specific subshell within an electron shell. Lastly, the spin number,

*m*

_{s}_{ }denotes the spin of a specific electron. Since only two electrons can occupy any one orbital, this number is usually represented as an up arrow or a down arrow (or a positive sign or a negative sign).

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