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?

  • A2
  • B 1 2
  • C4
  • D 1 4
  • E1

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 . 2 9 Ɨ 1 0 ļŠ± 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 = 4 šœ‹ šœ– ā„ š‘› š‘š š‘ž ļŠ ļŠ¦ ļŠØ ļŠØ ļŒ¾ ļŠØ ļŒ¾ , where š‘Ÿ ļ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‘š ļŒ¾ is the mass of the electron, and š‘ž ļŒ¾ 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 . 8 5 Ɨ 1 0 ļŠ± ļŠ§ ļŠØ Fā‹…māˆ’1 for the permittivity of free space, 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s for the reduced Planck constant, 9 . 1 1 Ɨ 1 0 ļŠ± ļŠ© ļŠ§ kg for the rest mass of an electron, and 1 . 6 0 Ɨ 1 0 ļŠ± 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 . 1 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s. Under the Bohr model of the atom, what energy level is the electron in? Use a value of 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s for the reduced Planck constant.

  • A3
  • B4
  • C6
  • D1
  • E2

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 . 0 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s for the reduced Planck constant.

  • A 4 . 2 0 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s
  • B 1 . 6 7 Ɨ 1 0 ļŠ± ļŠ© ļŠ« Jā‹…s
  • C 2 . 1 0 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s
  • D 6 . 6 3 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s
  • E 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ 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 = 4 šœ‹ šœ– ā„ š‘š š‘ž ļŠ¦ ļŠ¦ ļŠØ ļŒ¾ ļŠØ ļŒ¾ . Calculate the value of the Bohr radius. Use a value of 8 . 8 5 Ɨ 1 0 ļŠ± ļŠ§ ļŠØ Fā‹…māˆ’1 for the permittivity of free space, 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s for the reduced Planck constant, 9 . 1 1 Ɨ 1 0 ļŠ± ļŠ© ļŠ§ kg for the rest mass of an electron, and 1 . 6 0 Ɨ 1 0 ļŠ± ļŠ§ ļŠÆ C for the charge of an electron. Give your answer to 3 significant figures.

  • A 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ§ ļŠ§ m
  • B 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ§ ļŠ¦ m
  • C 5 . 2 6 Ɨ 1 0 ļŠ± ļŠ§ ļŠ§ m
  • D 2 . 1 0 Ɨ 1 0 ļŠ± ļŠ§ ļŠ¦ m
  • E 5 . 2 6 Ɨ 1 0 ļŠ± 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?

  • A 1 2
  • B1
  • C4
  • D 1 4
  • E2

Q9:

Use the formula š‘Ÿ = 4 šœ‹ šœ– ā„ š‘› š‘š š‘ž ļŠ ļŠ¦ ļŠØ ļŠØ ļŒ¾ ļŠØ ļŒ¾ , where š‘Ÿ ļ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‘š ļŒ¾ is the mass of the electron, and š‘ž ļŒ¾ 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 . 8 5 Ɨ 1 0 ļŠ± ļŠ§ ļŠØ F/m for the permittivity of free space, 1 . 0 5 Ɨ 1 0 ļŠ± ļŠ© ļŠŖ Jā‹…s for the reduced Planck constant, 9 . 1 1 Ɨ 1 0 ļŠ± ļŠ© ļŠ§ kg for the rest mass of an electron, and 1 . 6 0 Ɨ 1 0 ļŠ± 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?

  • A1
  • B4
  • C 1 4
  • D 1 2
  • E2

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