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Wize University Chemistry Textbook > Early Atomic Theory to Quantum Theory

How Atomic Spectra Relates to Electronic Transitions + Other Applications of the Bohr Model

Bohr Model EquationsPrevious Section
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Atomic Line Spectra

Emission and Absorption


Note: n=1 is ground state, all other n levels are excited states

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Emission Spectra




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Relating Electronic Transitions to Emission Spectra

Bohr Model of the Hydrogen Atom




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Hydrogen Emission Spectral Series:




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Example: Removing an Electron

What wavelength of light corresponds to the 4th ionization energy of Beryllium?

Can start by solving for the energy difference for this transition:

The 4th I.E. of Be corresponds to Be3+→Be4+Be^{3+}\rightarrow Be^{4+}, which is a transition from n = 1 to n = infinity for a one-electron species Be3+Be^{3+}.

Therefore,

ΔE=−2.178 ×10−18J(Z2) (1nf2−1ni2)\Delta E=-2.178\ \times10^{-18}J\left(Z^2\right)\ \left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)
=−2.178×10−18J×(42)(−112)=-2.178\times 10^{-18}J\times (4^2)\big(\frac{-1}{1^2}\Big)

ΔE=3.485×10−17J\Delta E=3.485\times 10^{-17}J


Now you can solve for the wavelength that the energy difference corresponds to:
λ=hcΔE=(6.626×10−34m2kg/s)(3.00×108m/s)3.485×10−17J\lambda=\frac{hc}{\Delta E}=\frac{(6.626\times10^{-34}m^2kg/s)(3.00\times10^8m/s)}{3.485\times10^{-17}J}
λ=5.704x10-9 m

1nm=1x10-9m
Divide meters value by 1x10-9 to get nm

λ=5.704nm

Practice: Understanding Emissions


Which of the following transitions would emit the shortest wavelength photon?

You shine light through a sample of gaseous atomized hydrogen and take an absorption spectrum as shown below. Only transitions to or from the ground state (n=1) appear in the spectrum. Which of these energy-level transitions correspond to the line labelled X in the absorption spectrum?



Extra Practice
Bohr model: Absorption/Emission Spectra
An Emission spectrum for a one-electron species is shown below. The spectrum shows all lines resulting from transitions to the second excited state. The line B is 165nm.
Identify the species in the spectrum above
Bohr model
Which of the following transitions would emit the shortest wavelength photon?
Bohr Model: Emission/Absorption Spectra
Consider the generic atomic emission line spectrum and the energy diagram shown below for a species (atom or ion) with one electron.
Which emission line has the highest energy?
Bohr Model: Frequency of light
Calculate the frequency of light, in Hz, required to promote gaseous He+ ions from the first excited state to the second excited state.
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states form n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What is the wavelength of the highest energy photon emitted?
h = 6.626 × 10-34 J s ( J = kg m2 s-2)
c = 2.9979 × 108 m s-1
H-like system
Which of the following electron transitions for the hydrogen atom is associated with the longest photon wavelength?
H-line spectra
An electronic transition of the one electron version of B, to the 2nd excited state, generates a line with wavelength 43.7 nm. Identify the transition.
Electromagnetic Radiation: Absorption Spectrum
You shine light through a sample of gaseous atomized hydrogen and take an absorption spectrum as shown below. Only transitions to or from the ground state (n=1) appear in the spectrum. Which of these energy-level transitions correspond to the line labelled X in the absorption spectrum?
Ionization Energy: Hydrogen
What is the ionization energy for H if its electron is in ground state?
The easiest way to solve this problem is by using the Rydberg expression:
1lambda=R(1n12−1n22)\frac{1}{lambda}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)
Bohr model: Transition Wavelength
What is the wavelength of photon that must be absorbed by a hydrogen atom to
promote its electron from the n=3n = 3 to the n=7n = 7 level?
Bohr Model
For a collection of hydrogen atoms, if one excites their electrons to energy state n = 3, when these electrons relax back to ground state, how many photons of different energy can be emitted?
Bohr Model: Frequency of light
Calculate the frequency of light, in Hz, required to promote gaseous He+ ions from the first excited state to the second excited state.
Bohr model: Absorption/Emission Spectra
An Emission spectrum for a one-electron species is shown below. The spectrum shows all lines resulting from transitions to the second excited state. The line B is 165nm.
Identify the species in the spectrum above
Bohr Model: Frequency of emission and photoelectric effect
Calculate the frequency of light, in Hz, emitted when gaseous Be3+ ions move form n = 4 to the n = 1 state?
Calculate the frequency (Hz) and wavelength (nm) of the emitted photon when an electron drops from the n = 6 to the n = 3 level in a hydrogen atom.
Practice: H-line Spectrum
A light generated due to an electronic transition between n=3 to n=1 of Li2+ is shone on a Mg metal surface. What is the maximum kinetic energy of the emitted electrons in Joules? wMg = 3.66 eV; 1 eV = 1.60218 ⋅\cdot 10−19 J
Electromagnetic Radiation
An excited hydrogen atom emits light with a wavelength of 433.9 nm to reach the energy level for which n = 2. In which principal quantum number did the electron begin?
CHEM 1011 (Dalhousie) - Electromagnetic Radiation
An electron in a hydrogen atom is promoted from the n = 1 state to a higher energy state when it absorbs radiation with a wavelength of 97.2 nm.
a) Calculate the frequency of the absorbed radiation.
b) Calculate the energy of the absorbed radiation.
Electromagnetic Radiation
7. An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the energy level for which n = 2. In which principal quantum number did the electron begin?
Electromagnetic Radiation
5. Which of the following statements are true?
Electromagnetic Radiation and Atoms
A student observes a hydrogen Atom emits a photon of light with energy of -4.09 x 10-19 J. The student notes that the emission falls within the visible light region of the electromagnetic spectrum, meaning the final state of the electron is in the Balmer series and thus nf = 2. Based on the students observations...
a) Calculate the wavelength, in nm, of the photon emitted by the hydrogen atom. Round your answer to the nearest whole number.
b) What is the initial state, ni, of the electron before relaxation?
Below is the energy level diagram for the possible energy levels of a hydrogen atom (not to scale).
Answer following question about the hydrogen atom.
What is the wavelength of light emitted by the transition labelled D from the shown figure?
Bohr Model
Given the atomic spectrum of hydrogen below, which of the following statements is correct?
Bohr Model: Emission/Absorption Spectra
Consider the generic atomic emission line spectrum and the energy diagram shown below for a species (atom or ion) with one electron.
Which emission line has the highest energy?
Bohr Model: Frequency of light
Calculate the frequency of light, in Hz, emitted when gaseous Be3+ ions move form n = 4 to the n = 1 state? Just enter the numerical value as your answer with 3 digits (don't write units). Units are Hz.
An emission spectrum for a one-electron species is shown below. All the lines correspond to transitions ending at the energy level n = 3. Line B has a wavelength of 165 nm. Identify the species that produced this spectrum.
Identify the species in the spectrum above
Bohr Model
A photon of light was released by a helium cation (He+) with an energy of 1.8312 x 10-18 J. If this transition ended at n = 2, from which level did this transition begin?
Bohr Model: Atomic Spectra
Using Bohr’s model of hydrogen atom, can you show that no electron transitions states relaxing to a final state of n ≥3 is capable of emitting photons with a wavelength in the visible spectrum?
Calculate the wavelength of light emitted when an electron in a hydrogen atom moves from n= 1 to n = 2
The energy level diagram for an electron in a hydrogen atom (not to scale) is shown below. Answer following question with reference to this diagram.
Which transition represents the ionization of the hydrogen atom?
The Bohr Model
A photon of light was released by a hydrogen atom with an energy of 1.94 x 10-18 J. If this transition ended at n = 1, from which level did this transition begin?
How much energy would be required to completely remove an electron from the n=3 shell of a hydrogen atom?
A sample of hydrogen atoms are excited to an unknown energy level. The excited electrons relax to the ground state (n = 1) and emit a photon with a wavelength of 103nm. What energy level were the electrons in the hydrogen atom originally excited to?
Bohr model: Wavelength
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states form n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What is the wavelength of the highest energy photon emitted?
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states form n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What is the wavelength of the highest energy photon emitted?
h = 6.626 × 10-34 J s ( J = kg m2 s-2)
c = 2.9979 × 108 m s-1
An emission spectra is recorded from a sample of hydrogen. The discreet lines in the spectra come from:
Bohr model
Which of the following transitions would emit the shortest wavelength photon?
Bohr Model: Energy
Which hydrogen emission line should you expect to have the greatest energy?
Bohr model: Energy
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states from n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What transition produces the lowest energy photon?
Bohr model: Finding the Initial Energy Level
In the atomic emission spectra for hydrogen a line is observed at 97.25nm. What was the initial energy level for the electron before the transition occurred? The transition ends at the ground state.
Bohr model: Qualitative Emissions
Which of the following transitions would emit the shortest wavelength photon?
Periodic Trends: Ionization of an Excited Hydrogen Atom
A sample of hydrogen atoms is thermally excited so that the electrons are resting in the n=3 state. What is the wavelength of the lowest energy photon capable of ionizing these excited hydrogen atoms?
Bohr Model: Predicting Hydrogen Emission Wavelengths
Calculate the wavelength of light emitted when an electron in a hydrogen atom moves from n= 2 to n = 1.
Shown below is an energy level diagram for a hydrogen atom. Calculate the frequency of the photon associated with transition E
Shown below is an energy level diagram for a hydrogen atom. Calculate the Energy of the photon associated with transition B
Shown below is an energy level diagram for a hydrogen atom. Please choose the INCORRECT statement
Shown below is an energy level diagram for a hydrogen atom. Please choose the CORRECT statement
What is the energy change when an electron moves from the n = 7 to n = 2 energy level in a hydrogen atom?
A sample of Hydrogen atoms is excited to n = 6 and the sample is then allowed to relax back to the ground state (n = 1) and an emission spectrum is recorded. What is the wavelength photon emitted?
Bohr Model: Absorption Spectrum
You shine light through a sample of gaseous atomized hydrogen and take an absorption spectrum as shown below. Only transitions to or from the ground state (n=1) appear in the spectrum. Which of these energy-level transitions correspond to the line labelled X in the absorption spectrum?
Atom: Calculating Ionization Energy of a Hydrogen-like Ion
Calculate the ionization energy of He+. Express your answer in Joules (J).