Free Quantum Numbers MCQs with Answers

1. The principal quantum number n of an electron determines its

• A. shape of orbital
• B. main energy level and distance from the nucleus
• C. orientation of the orbital in space
• D. direction of spin

Explanation: The principal quantum number sets the shell, and therefore the main energy level and the average distance of the electron from the nucleus. Orbital shape is given by the azimuthal quantum number l, orientation by the magnetic quantum number m, and spin by s, which takes the values plus or minus one half.

2. How many orbitals are present in the d subshell?

• A. Three
• B. Five
• C. Seven
• D. Nine

Explanation: For the d subshell l equals 2, so m runs from minus 2 to plus 2, giving five values and therefore five orbitals. With two electrons per orbital the d subshell holds a maximum of ten electrons, which is exactly the width of the d block in the periodic table. The p subshell has three orbitals and the f subshell has seven.

3. Which set of quantum numbers is not possible?

• A. n = 2, l = 1, m = 0
• B. n = 3, l = 2, m = -2
• C. n = 2, l = 2, m = 1
• D. n = 4, l = 0, m = 0

Explanation: The azimuthal quantum number l is restricted to values from 0 up to n minus 1, so with n equal to 2 the only allowed values of l are 0 and 1. A set with n equal to 2 and l equal to 2 would describe a 2d orbital, which does not exist. Every other set listed satisfies both that rule and the requirement that m lies between minus l and plus l.

4. The maximum number of electrons that can occupy the shell with n = 3 is

• A. 8
• B. 10
• C. 18
• D. 32

Explanation: The capacity of a shell is 2n squared, so for n equal to 3 that is 2 times 9, which is 18. Those 18 are distributed as 2 in the 3s, 6 in the 3p and 10 in the 3d subshells. The answer 8 is the common trap, taken from the octet rule rather than from the shell capacity.

5. The principal quantum number n determines

• A. the shape of the orbital
• B. the main energy level and the average distance of the electron from the nucleus
• C. the orientation of the orbital in space
• D. the direction of electron spin

Explanation: The value of n fixes the shell, so a larger n means a higher energy and an electron held further out on average. Shape is set by the azimuthal quantum number l, orientation by the magnetic quantum number m, and spin by s. Knowing which of the four quantum numbers controls which property answers a large family of questions.

6. For n equals 3, the possible values of the azimuthal quantum number l are

• A. 0 only
• B. 0 and 1
• C. 0, 1 and 2
• D. 1, 2 and 3

Explanation: The azimuthal quantum number runs from 0 up to n minus 1, so for the third shell it takes the values 0, 1 and 2, corresponding to the 3s, 3p and 3d subshells. It never equals n itself, which rules out the last option. This is why the first shell has only an s subshell.

7. The maximum number of electrons that can occupy the third shell is

• A. 8
• B. 18
• C. 32
• D. 2

Explanation: Shell capacity is 2n squared, so for n equal to 3 the maximum is 2 multiplied by 9, that is 18, made up of 2 in 3s, 6 in 3p and 10 in 3d. The figure 8 is the octet that fills only the s and p subshells, which is why it is the tempting answer. The fourth shell holds 32 by the same formula.

8. The magnetic quantum number m for an electron in a 2p subshell can take the values

• A. 0 only
• B. minus 1, 0 and plus 1
• C. minus 2 to plus 2
• D. plus 1 only

Explanation: The magnetic quantum number runs from minus l to plus l, and for a p subshell l equals 1, giving three values that correspond to the three perpendicular orientations of the p orbital. A d subshell with l equal to 2 would give five values. The number of values is always 2l plus 1.

9. Which set of quantum numbers is not permitted?

• A. n equals 2, l equals 1, m equals 0
• B. n equals 3, l equals 2, m equals minus 2
• C. n equals 2, l equals 2, m equals 1
• D. n equals 1, l equals 0, m equals 0

Explanation: The azimuthal quantum number can never equal or exceed n, so l equal to 2 is impossible when n is 2, which would describe a non existent 2d orbital. The other three sets satisfy every restriction. Checking l against n first, then m against l, catches almost every invalid set.

10. Which set of quantum numbers is not allowed for an electron?

• A. n=2, l=1, m=0, s=+1/2
• B. n=3, l=0, m=0, s=-1/2
• C. n=2, l=2, m=1, s=+1/2
• D. n=1, l=0, m=0, s=+1/2

Explanation: The azimuthal quantum number can only run from 0 up to n minus 1, so with n equal to 2 the value of l cannot reach 2, and the set describes a non existent 2d orbital. The other three sets satisfy every restriction, including that m lies between minus l and plus l. Checking l against n first, then m against l, resolves questions of this type quickly.