Lesson Worksheet: The Bohr Model of the Atom Physics • 9th Grade

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

Q1:

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

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 5.29×10 m for the Bohr radius.

Q3:

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

Q4:

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 𝑎=4𝜋𝜖𝑚𝑞. Calculate the value of the Bohr radius. Use a value of 8.85×10 F⋅m−1 for the permittivity of free space, 1.05×10 J⋅s for the reduced Planck constant, 9.11×10 kg for the rest mass of an electron, and 1.60×10 C for the charge of an electron. Give your answer in scientific notation to two decimal places.

  • A1.05×10 m
  • B5.26×10 m
  • C5.26×10 m
  • D2.10×10 m
  • E1.05×10 m

Q5:

Use the formula 𝑟=4𝜋𝜖𝑛𝑚𝑞, where 𝑟 is the orbital radius of an electron in energy level 𝑛 of a hydrogen atom, 𝜖 is the permittivity of free space, is the reduced Planck constant, 𝑚 is the mass of the electron, and 𝑞 is the charge of the electron, to calculate the orbital radius of an electron that is in energy level 𝑛=4 of a hydrogen atom. Use a value of 8.85×10 F⋅m−1 for the permittivity of free space, 1.05×10 J⋅s for the reduced Planck constant, 9.11×10 kg for the rest mass of an electron, and 1.60×10 C for the charge of an electron. Give your answer to two decimal places.

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 1.05×10 J⋅s for the reduced Planck constant.

  • A2.10×10 J⋅s
  • B1.05×10 J⋅s
  • C6.63×10 J⋅s
  • D4.20×10 J⋅s
  • E1.67×10 J⋅s

Q7:

An electron in a hydrogen atom has an angular momentum of 3.15×10 J⋅s. Under the Bohr model of the atom, what energy level is the electron in? Use a value of 1.05×10 J⋅s for the reduced Planck constant.

Q8:

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?

Q9:

Use the formula 𝑟=4𝜋𝜖𝑛𝑚𝑞, where 𝑟 is the orbital radius of an electron in energy level 𝑛 of a hydrogen atom, 𝜖 is the permittivity of free space, is the reduced Planck constant, 𝑚 is the mass of the electron, and 𝑞 is the charge of the electron, to calculate the orbital radius of an electron that is in energy level 𝑛=2 of a hydrogen atom. Use a value of 8.85×10 F/m for the permittivity of free space, 1.05×10 J⋅s for the reduced Planck constant, 9.11×10 kg for the rest mass of an electron, and 1.6×10 C for the charge of an electron. Give your answer to two decimal places.

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

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