Lesson Worksheet: Quantum Numbers Chemistry

In this worksheet, we will practice using quantum numbers to describe an electron within an atom.


The quantum numbers for three electrons in an atom of silicon are shown. What is the correct order from lowest to highest energy of these electrons?

  1. 𝑛=2,𝑙=1,𝑚=+1,𝑚=12
  2. 𝑛=3,𝑙=1,𝑚=1,𝑚=12
  3. 𝑛=2,𝑙=0,𝑚=0,𝑚=+12
  • A3, 1, 2
  • B2, 3, 1
  • C2, 1, 3
  • D1, 2, 3
  • E3, 2, 1


Which of these sets of four quantum numbers does not exist?

  • A𝑛=2, 𝑙=2, 𝑚=0, 𝑚=+12
  • B𝑛=3, 𝑙=2, 𝑚=1, 𝑚=+12
  • C𝑛=1, 𝑙=0, 𝑚=0, 𝑚=+12
  • D𝑛=4, 𝑙=3, 𝑚=2, 𝑚=+12


If 𝑛=1, how many possible values of 𝑙 are there?


How many electrons in total can have the quantum numbers 𝑛=2 and 𝑙=1?


The quantum numbers for the valence electron in an atom of lithium are 𝑛=2, 𝑙=0, 𝑚=0, and 𝑚=+12. What are the quantum numbers for the second valence electron in an atom of beryllium?

  • A𝑛=2, 𝑙=1, 𝑚=0, and 𝑚=12
  • B𝑛=3, 𝑙=0, 𝑚=0, and 𝑚=+12
  • C𝑛=2, 𝑙=0, 𝑚=0, and 𝑚=12
  • D𝑛=2, 𝑙=0, 𝑚=1, and 𝑚=+12
  • E𝑛=3, 𝑙=0, 𝑚=0, and 𝑚=12


If 𝑙=0, how many possible values of 𝑚 are there?


How many electrons can have a principal quantum number (𝑛) equal to 1?


What is the relationship between the principal quantum number, 𝑛, and the total number of orbitals?

  • A𝑛
  • B𝑛2
  • C𝑛
  • D2𝑛
  • E2𝑛+1


Two electrons, A and B, have the same energy. Electron A has the quantum numbers 𝑛=4,𝑙=3,𝑚=+1, 𝑚=+12. What are the quantum numbers of the electron B, knowing that it spins in the opposite direction?

  • A𝑛=4,𝑙=3,𝑚=+1,𝑚=+12
  • B𝑛=3,𝑙=2,𝑚=+1,𝑚=+12
  • C𝑛=4,𝑙=3,𝑚=+1,𝑚=12
  • D𝑛=3,𝑙=2,𝑚=+1,𝑚=12


Which of the following is correct when two electrons of an atom have the same 𝑙 and 𝑚 values?

  • AThey must be located in the same energy level.
  • BThey can not have the same 𝑚 and 𝑛 values at the same time.
  • CThey are not located in the same energy sublevel.
  • DThey must have the same spin direction.

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