Worksheet: Energy Levels in the Bohr Model

In this worksheet, we will practice using the Bohr model to calculate the energies of electron shells in hydrogenic atoms.

Q1:

The electron in a hydrogen atom occupies the energy level with 𝑛 = 3. Calculate the ionization energy of this atom.

  • A 1 . 4 5 3 × 1 0 J
  • B 8 . 0 7 9 × 1 0 J
  • C 1 . 9 3 8 × 1 0 J
  • D 7 . 2 6 6 × 1 0 J
  • E 2 . 4 2 2 × 1 0 J

Q2:

The electron in a He+ ion occupies the energy level with 𝑛=7. Calculate the ionization energy of this atom.

  • A 8 . 8 9 7 × 1 0 J
  • B 2 . 6 7 0 × 1 0 J
  • C 4 . 4 4 9 × 1 0 J
  • D 1 . 7 7 9 × 1 0 J
  • E 1 . 2 4 6 × 1 0 J

Q3:

The electron in the 𝑛 = 4 energy level of a hydrogen atom absorbs a photon and is promoted to the energy level with 𝑛 = 6. Calculate, to 3 significant figures, the wavelength of the absorbed photon.

  • A 9 . 3 7 × 1 0 m
  • B 1 . 0 9 × 1 0 m
  • C 4 . 5 6 × 1 0 m
  • D 4 . 5 6 × 1 0 m
  • E 2 . 6 2 × 1 0 m

Q4:

The electron in the 𝑛=3 energy level of a He+ ion absorbs a photon and is promoted to the energy level with 𝑛=5. Calculate the wavelength of the absorbed photon to 3 significant figures.

  • A 3 . 4 2 × 1 0 m
  • B 1 . 7 1 × 1 0 m
  • C 6 . 4 1 × 1 0 m
  • D 1 . 8 2 × 1 0 m
  • E 3 . 2 0 × 1 0 m

Q5:

An electron in an excited hydrogen atom occupies the 𝑛=2 energy level. Using the Bohr model, calculate the ionization energy for the excited hydrogen atom.

  • A 1 . 0 9 0 × 1 0 J
  • B 7 . 2 6 6 × 1 0 J
  • C 2 . 7 2 5 × 1 0 J
  • D 5 . 4 5 0 × 1 0 J
  • E 2 . 4 2 2 × 1 0 J

Q6:

An electron in a hydrogen atom moves from the 𝑛=5 energy level to the 𝑛=2 energy level. Using the Bohr model, calculate the energy of the photon produced by this transition.

Q7:

Using the Bohr model, calculate the energy of an electron in the 𝑛=4 energy level of the Li2+ ion.

  • A 4 . 9 0 5 × 1 0 J
  • B 5 . 4 5 0 × 1 0 J
  • C 1 . 6 3 5 × 1 0 J
  • D 3 . 8 7 5 × 1 0 J
  • E 1 . 2 2 6 × 1 0 J

Q8:

Using the Bohr model, calculate, to 4 significant figures, the lowest possible energy of an electron in the He+ ion.

  • A 5 . 4 5 0 × 1 0 J
  • B 8 . 7 1 9 × 1 0 J
  • C 1 . 0 9 0 × 1 0 J
  • D 4 . 3 6 0 × 1 0 J
  • E 2 . 1 8 0 × 1 0 J

Q9:

Using the Bohr model, calculate the energy of an electron in the 𝑛=8 energy level of the hydrogen atom.

  • A 6 . 8 1 2 × 1 0 J
  • B 3 . 4 0 6 × 1 0 J
  • C 2 . 1 4 6 × 1 0 J
  • D 1 . 3 6 2 × 1 0 J
  • E 2 . 7 2 4 × 1 0 J

Q10:

The electron in the 𝑛=3 energy level of a Li2+ ion absorbs a photon and is promoted to the energy level with 𝑛=6. In which of the following transitions would an electron absorb a photon of the same energy?

  • APromotion of an electron from 𝑛=2 to 𝑛=8 in the He+ ion
  • BPromotion of an electron from 𝑛=2 to 𝑛=4 in the He+ ion
  • CPromotion of an electron from 𝑛=2 to 𝑛=4 in the hydrogen atom
  • DPromotion of an electron from 𝑛=2 to 𝑛=8 in the hydrogen atom
  • EPromotion of an electron from 𝑛=1 to 𝑛=2 in the He+ ion

Q11:

Which of the following ions would have the same ionization energy as a hydrogen atom with an electron in the 𝑛=4 energy level?

  • AA Li2+ ion with an electron in the 𝑛=18 energy level
  • BA Li2+ ion with an electron in the 𝑛=12 energy level
  • CA He+ ion with an electron in the 𝑛=12 energy level
  • DA He+ ion with an electron in the 𝑛=6 energy level
  • EA Be3+ ion with an electron in the 𝑛=18 energy level

Q12:

The atomic emission spectra for the atoms of four elements are shown.

Which transition is responsible for the line at 489 nm in the hydrogen spectrum?

  • A 𝑛 = 3 to 𝑛=2
  • B 𝑛 = 4 to 𝑛=2
  • C 𝑛 = 3 to 𝑛=1
  • D 𝑛 = 5 to 𝑛=2
  • E 𝑛 = 4 to 𝑛=3

In which of these atoms does an electronic transition produce a photon with an energy of 4.506×10 J?

  • A C a
  • BNone of these atoms
  • C H g
  • D H
  • E N a

Which of these spectra contains lines at both 613 THz and 518 THz?

  • ANone of these spectra
  • B N a
  • C C a
  • D H g
  • E H

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