Worksheet: Quantum Numbers

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In this worksheet, we will practice assigning quantum numbers to atomic orbitals and relating these values to the orbital nodes, energies, and degeneracies.

Q1:

What percentage of the orbitals in the 𝑛=4 shell of an atom are d orbitals?

Q2:

Which subshell is occupied by electrons with quantum numbers 𝑛=3 and 𝑙=1?

  • A3s
  • B3p
  • C4s
  • D4d
  • E4p

Q3:

Which subshell is occupied by electrons with quantum numbers 𝑛=5 and 𝑙=3?

  • A6d
  • B5d
  • C5f
  • D4f
  • E6f

Q4:

Which subshell is occupied by electrons with the quantum numbers 𝑛=2 and 𝑙=0?

  • A1s
  • B3p
  • C2s
  • D3s
  • E2p

Q5:

What is the maximum number of electrons that can occupy a shell with 𝑛=2?

Q6:

What is the maximum number of electrons that can occupy a shell with 𝑛=5?

Q7:

What is the maximum number of electrons that can occupy a shell with quantum number 𝑛?

  • A2𝑛
  • B2𝑛
  • C𝑛
  • D𝑛+𝑛
  • E𝑛

Q8:

What is the principal quantum 𝑛 for a shell that can be occupied by a maximum of 32 electrons?

Q9:

How many radial nodes are displayed by the 4f orbital?

Q10:

How many radial nodes are displayed by an orbital with 𝑛=4 and 𝑙=1?

Q11:

How many radial nodes are displayed by an orbital with 𝑛=7 and 7 possible values of 𝑚?

Q12:

What is the value of 𝑙 for an orbital with 𝑛=5 and 2 radial nodes?

Q13:

What is the value of 𝑛 for an orbital with 1 radial node and 5 possible values of 𝑚?

Q14:

How many radial nodes are displayed by an orbital with the quantum numbers 𝑛 and 𝑙?

  • A𝑛+𝑙−1
  • B𝑛−𝑙+1
  • C𝑛−𝑙
  • D𝑛−𝑙−1
  • E𝑛+𝑙

Q15:

For electrons in an atom or ion, which of the following quantum numbers does not adopt an integer value?

  • A𝑛
  • B𝑚
  • C𝑚
  • D𝑙

Q16:

Which of the following quantum numbers determines the shape of an atomic orbital?

  • A𝑚
  • B𝑙
  • C𝑚
  • D𝑛
  • E𝑗

Q17:

If two orbitals have the same values of 𝑛 and 𝑙 but different values of 𝑚, in what way do they differ?

  • AOrbital angular momentum
  • BSpin
  • COrientation
  • DEnergy
  • EShape

Q18:

Which of the following statements is false?

  • ADifferent orbitals in the same subshell always have different values of 𝑗.
  • BOrbitals in different subshells of the same shell can have the same energy.
  • COrbitals in different subshells of the same shell can have the same value of 𝑚.
  • DDifferent orbitals in the same subshell always have different values of 𝑚.
  • EOrbitals in different subshells of the same shell cannot have the same value of 𝑙.

Q19:

Which of the following statements is false?

  • AThe magnetic quantum number cannot be greater in magnitude than the azimuthal quantum number.
  • BThe total angular momentum can be greater than the azimuthal quantum number.
  • CThe number of subshells in a shell is equal to the principal quantum number.
  • DThe number of orbitals in a subshell is equal to twice the principal quantum number plus one.
  • EThe spin projection quantum number for an electron only has two possible values.

Q20:

Which subshell is occupied by electrons with the quantum numbers 𝑛=2 and 𝑙=1?

  • A2s
  • B2p
  • C3p
  • D1s
  • E3s

Q21:

Which subshell is occupied by electrons with the quantum numbers 𝑛=4 and 𝑙=2?

  • A4s
  • B4p
  • C4d
  • D3p
  • E3d

Q22:

Which subshell is occupied by electrons with the quantum numbers 𝑛=6 and 𝑙=0?

  • A6s
  • B5s
  • C6p
  • D5p
  • E7s

Q23:

How many degenerate orbitals are present in the 2s subshell?

Q24:

How many degenerate orbitals are present in the 6p subshell?

Q25:

Which subshell is occupied by electrons with the quantum numbers 𝑛 = 3 and 𝑙 = 2?

  • A3d
  • B2p
  • C3p
  • D3s
  • E2s

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