Bohr Equation Practice Problems

Calculate the wavelength (m) of light emitted when an electron of a hydrogen atom drops from 4d to 3p.

The Bohr model of atomic structure is described by the following equation 

where Z is the charge on the nucleus, a₀ is the Bohr radius, r is the radius of the orbit, and n is a positive integer similar to the principal quantum number. Based on this model, electrons are bound to orbit a nucleus at specific distances. Bohr concluded that the energy level E of an electron in a certain orbit is 

where e is the electron's charge. 

Illustrate the energy difference between any two energy levels by creating your own equation and comparing it to the Balmer-Rydberg equation.

The electron in an energetically excited hydrogen atom is located in the 5f subshell. A photon is released as the electron descends to the 4d subshell. How much energy is required to remove the electron in the 4d subshell?

An equation resembling the Balmer-Rydberg equation shown below, where Z is the atomic number, can be used to describe the orbital energies of single-electron atoms or ions, such as Li⁺. 

What wavelength of light in nanometers is released when the electron in Li⁺ falls from n = 4 to n = 2?

What is the wavelength in nanometers of the spectral line for hydrogen when an electron transitions from n_f = 5 to n_i = 2 using the Balmer equation? What is the energy of the radiation corresponding to this line in kilojoules per mole?

What is the wavelength in nm needed to remove an electron from the fourth shell (n=4) of a hydrogen atom (R_∞ = 1.097×10⁻² nm⁻¹)? How much energy in kJ/mol is needed?

What is the wavelength of light, in nanometers, emitted when an electron in a hydrogen atom transitions from an orbital in n = 6 to n = 3?

An electron in a hydrogen atom is excited from n = 1 to n = ∞. Consider a situation wherein light with a wavelength shorter than the required for the transition is absorbed and relate this with the plot shown below.

Radiation with a wavelength of 92.315 nm is emitted by a hydrogen atom. What are the initial and final n values that correspond to this emission?

An electron relaxes to n = 4, releasing a photon with a frequency of 69 THz. Determine the energy level the electron originated.

For the Balmer series (n_f = 2), what are the wavelengths in nm of the emission lines for n _i = 6, 7, 8?

For the Lyman series (n_f = 1), what are the wavelengths in nm of the emission lines for n _i = 5, 6, 7?

Which statement is true regarding the excitation of an electron in a hydrogen atom from n = 1 to n = ∞ ?

Determine the difference in energy between the ground state and excited state of a laser if the excitation gives off 348 nm photons as excess energy.

From n = 5, an electron of a hydrogen atom emits 4322 nm. Determine the final energy level of the electron.

Determine the transitions of each wavelength observed from the atomic emission spectrum of hydrogen 

92.63 nm, 94.98 nm, 121.6 nm

For the following electronic transitions in a hydrogen atom, find the frequency of the light emitted:

a. n = 3 → n = 2
b. n = 6 → n = 4
c. n = 4 → n = 1
d. n = 5 → n = 2

Three wavelengths are observed from an atomic emission spectrum of hydrogen. They are 97.23 nm, 102.6 nm, and 94.96 nm. What is their corresponding electronic transition?

Determine the initial principal quantum level of an electron that emits a wavelength of 486.2 nm when excited from n = 2.

What is the energy in Joules needed to excite a hydrogen atom via an electronic transition from n = 1 to n =3 principal energy level?

Determine the wavelengths (in nm) of the emission lines in the Brackett series (n_f = 4) when n_i = 6, 7, and 8.

Labeled A, B, C, and D in the diagram below are four electronic transitions in a hydrogen atom. Find the wavelength (nm) of the photon emitted for A, B, C, and D. Identify which transition/s lead/s to the emission of visible light.

Labeled A, B, C, and D in the diagram below are four electronic transitions in a hydrogen atom. Find the energy (J) of the photon emitted for A, B, C, and D.

What is the wavelength of the light emitted when an electron in a hydrogen atom transitions from n = 3 to n = 1? Where does the emitted light fall on the electromagnetic spectrum?

An electron in the n = 9 level of the hydrogen atom relaxes to a lower energy level, emitting light of 923 nm. What is the value of n for the level to which the electron relaxed?

Arrange the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 6, n = 5 to n = 7, n = 2 to n = 4, and n = 1 to n = 2.