Worksheet: The Bohr Model of the Atom

In this worksheet, we will practice calculating the orbital radius of an electron in different energy levels of a hydrogen atom.

Q1:

If an electron had a charge that was twice its actual charge but the proton still had the same charge, according to the Bohr model of the atom, by what factor would the Bohr radius change?

  • A4
  • B2
  • C12
  • D1
  • E14

Q2:

If an electron in a hydrogen atom is at a distance of 1.32 nm from the nucleus, what energy level is it in? Use a value of 5.29Ɨ10ļŠ±ļŠ§ļŠ§ m for the Bohr radius.

Q3:

If the proton had a mass 1.5 times its actual value, according to the Bohr model of the atom, by what factor would the Bohr radius change?

Q4:

Use the formula š‘Ÿ=4šœ‹šœ–ā„š‘›š‘šš‘žļŠļŠ¦ļŠØļŠØļŒ¾ļŠØļŒ¾, where š‘ŸļŠ is the orbital radius of an electron in energy level š‘› of a hydrogen atom, šœ–ļŠ¦ is the permittivity of free space, ā„ is the reduced Planck constant, š‘šļŒ¾ is the mass of the electron, and š‘žļŒ¾ is the charge of the electron, to calculate the orbital radius of an electron that is in energy level š‘›=4 of a hydrogen atom. Use a value of 8.85Ɨ10ļŠ±ļŠ§ļŠØ Fā‹…māˆ’1 for the permittivity of free space, 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant, 9.11Ɨ10ļŠ±ļŠ©ļŠ§ kg for the rest mass of an electron, and 1.60Ɨ10ļŠ±ļŠ§ļŠÆ C for the charge of an electron. Give your answer to 3 significant figures.

Q5:

An electron in a hydrogen atom has an angular momentum of 3.15Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s. Under the Bohr model of the atom, what energy level is the electron in? Use a value of 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant.

Q6:

In the Bohr model of the atom, what is the magnitude of the angular momentum of an electron in a hydrogen atom in the ground state? Use a value of 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant.

  • A2.10Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s
  • B1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s
  • C6.63Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s
  • D4.20Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s
  • E1.67Ɨ10ļŠ±ļŠ©ļŠ« Jā‹…s

Q7:

The Bohr radius is a physical constant that is equal to the distance between the nucleus and the electron of a hydrogen atom in the ground state. Its value is given by the formula š‘Ž=4šœ‹šœ–ā„š‘šš‘žļŠ¦ļŠ¦ļŠØļŒ¾ļŠØļŒ¾. Calculate the value of the Bohr radius. Use a value of 8.85Ɨ10ļŠ±ļŠ§ļŠØ Fā‹…māˆ’1 for the permittivity of free space, 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant, 9.11Ɨ10ļŠ±ļŠ©ļŠ§ kg for the rest mass of an electron, and 1.60Ɨ10ļŠ±ļŠ§ļŠÆ C for the charge of an electron. Give your answer to 3 significant figures.

  • A1.05Ɨ10ļŠ±ļŠ§ļŠ¦ m
  • B5.26Ɨ10ļŠ±ļŠ§ļŠ¦ m
  • C5.26Ɨ10ļŠ±ļŠ§ļŠ§ m
  • D2.10Ɨ10ļŠ±ļŠ§ļŠ¦ m
  • E1.05Ɨ10ļŠ±ļŠ§ļŠ§ m

Q8:

If the electron had a mass that was twice its actual mass, according to the Bohr model of the atom, by what factor would the Bohr radius change?

  • A4
  • B2
  • C14
  • D12
  • E1

Q9:

Use the formula š‘Ÿ=4šœ‹šœ–ā„š‘›š‘šš‘žļŠļŠ¦ļŠØļŠØļŒ¾ļŠØļŒ¾, where š‘ŸļŠ is the orbital radius of an electron in energy level š‘› of a hydrogen atom, šœ–ļŠ¦ is the permittivity of free space, ā„ is the reduced Planck constant, š‘šļŒ¾ is the mass of the electron, and š‘žļŒ¾ is the charge of the electron, to calculate the orbital radius of an electron that is in energy level š‘›=2 of a hydrogen atom. Use a value of 8.85Ɨ10ļŠ±ļŠ§ļŠØ F/m for the permittivity of free space, 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant, 9.11Ɨ10ļŠ±ļŠ©ļŠ§ kg for the rest mass of an electron, and 1.60Ɨ10ļŠ±ļŠ§ļŠÆ C for the charge of an electron. Give your answer to 3 significant figures.

Q10:

If both the electron and the proton had charges that were twice the size of their actual charges, according to the Bohr model of the atom, by what factor would the Bohr radius change?

  • A12
  • B1
  • C2
  • D4
  • E14

Q11:

Use the formula š‘Ÿ=š‘Žš‘›ļŠļŠ¦ļŠØ, where š‘ŸļŠ is the orbital radius of an electron in energy level š‘› of a hydrogen atom and š‘ŽļŠ¦ is the Bohr radius, to calculate the orbital radius of an electron that is in energy level š‘›=3 of a hydrogen atom. Use a value of 5.29Ɨ10ļŠ±ļŠ§ļŠ§ m for the Bohr radius. Give your answer to 3 significant figures.

Q12:

In the Bohr model of the atom, what is the magnitude of the angular momentum of an electron in a hydrogen atom for which š‘›=2? Use a value of 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant.

  • A1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s
  • B2.10Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s
  • C2.65Ɨ10ļŠ±ļŠ©ļŠ© Jā‹…s
  • D1.33Ɨ10ļŠ±ļŠ©ļŠ© Jā‹…s
  • E4.20Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s

Q13:

An electron in a hydrogen atom has an angular momentum of 6.30Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s. Under the Bohr model of the atom, what energy level is the electron in? Use a value of 1.05Ɨ10ļŠ±ļŠ©ļŠŖ Jā‹…s for the reduced Planck constant.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.