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.

  • A1.453×10 J
  • B8.079×10 J
  • C1.938×10 J
  • D7.266×10 J
  • E2.422×10 J

Q2:

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

  • A8.897×10 J
  • B2.670×10 J
  • C4.449×10 J
  • D1.779×10 J
  • E1.246×10 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.

  • A9.37×10 m
  • B1.09×10 m
  • C4.56×10 m
  • D4.56×10 m
  • E2.62×10 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.

  • A3.42×10 m
  • B1.71×10 m
  • C6.41×10 m
  • D1.82×10 m
  • E3.20×10 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.

  • A1.090×10 J
  • B7.266×10 J
  • C2.725×10 J
  • D5.450×10 J
  • E2.422×10 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.

  • A4.905×10 J
  • B5.450×10 J
  • C1.635×10 J
  • D3.875×10 J
  • E1.226×10 J

Q8:

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

  • A5.450×10 J
  • B8.719×10 J
  • C1.090×10 J
  • D4.360×10 J
  • E2.180×10 J

Q9:

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

  • A6.812×10 J
  • B3.406×10 J
  • C2.146×10 J
  • D1.362×10 J
  • E2.724×10 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?

  • A𝑛=3 to 𝑛=2
  • B𝑛=4 to 𝑛=2
  • C𝑛=3 to 𝑛=1
  • D𝑛=5 to 𝑛=2
  • E𝑛=4 to 𝑛=3

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

  • ACa
  • BNone of these atoms
  • CHg
  • DH
  • ENa

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

  • ANone of these spectra
  • BNa
  • CCa
  • DHg
  • EH

Q13:

Shown in the figure are the electronic energy levels of the hydrogen atom. For how many lines in the atomic emission spectrum of hydrogen do electronic transitions occur from the level with energy 0.85 V?

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