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
  • B4p
  • C4s
  • D3p
  • E4d

Q3:

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

  • A6f
  • B5d
  • C6d
  • D5f
  • E4f

Q4:

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

  • A3s
  • B2p
  • C3p
  • D2s
  • E1s

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 ?

  • A 𝑛
  • B 𝑛 2
  • C 2 𝑛
  • D 2 𝑛 2
  • E 𝑛 + 𝑛 2

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 𝑙 ?

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 𝑙 ?

Q14:

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

  • A 𝑛 + 𝑙 − 1
  • B 𝑛 − 𝑙
  • C 𝑛 + 𝑙
  • D 𝑛 − 𝑙 − 1
  • E 𝑛 − 𝑙 + 1

Q15:

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

  • A 𝑙
  • B 𝑛
  • C 𝑚 𝑙
  • D 𝑚 𝑆

Q16:

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

  • A 𝑙
  • B 𝑛
  • C 𝑚 𝑙
  • D 𝑚 𝑆

Q17:

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

  • A 𝑚 𝑠
  • B 𝑛
  • C 𝑚 𝑙
  • D 𝑙
  • E 𝑗

Q18:

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

  • ASpin
  • BShape
  • CEnergy
  • DOrientation
  • EOrbital angular momentum

Q19:

Which of the following statements is false?

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

Q20:

Which of the following statements is false?

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

Q21:

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

  • A1s
  • B2s
  • C3s
  • D2p
  • E3p

Q22:

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

  • A4s
  • B4p
  • C3p
  • D4d
  • E3d

Q23:

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

  • A6p
  • B5s
  • C5p
  • D6s
  • E7s

Q24:

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

  • A3
  • B2
  • C5
  • D1
  • E7

Q25:

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

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