Ch.7 - Quantum MechanicsWorksheetSee all chapters
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Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
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Ch.7 - Quantum Mechanics
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Ch.10 - Molecular Shapes & Valence Bond Theory
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Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
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Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Jules Bruno

Bohr and Balmer equations

Both Bohr’s equation and Balmer’s equation try their best to describe and characterize changes in either energy or wavelength when a photon or an electron goes from one shell to another shell. 

Bohr equation

In the Bohr equation, we’re going to say this is an equation that relates energy to a photon electronic transitions. We’re going to say here we’re talking about an electron or photon going from one shell to another shell and how that affects the energy (either absorbed or released).

The equation is delta E = RH (1/n2final - 1/n2 initial). 

Here, our RH value is 2.18 x 10-18 Joules. We’d use this version of the Bohr equation when they’re giving us or discussing two shells like you’re going from shell 3 to shell 1 and they reference energy. Again, if they’re talking about two shells, and they’re referencing energy, we use Bohr’s equation. 

Balmer rydberg equation

In Balmer’s equation, this equation relates wavelength to a photon’s electronic transitions. In the above example, it tries to relate changes in your shell number to the wavelength. Here, R now becomes 1.0974 x 107 m-1. Realize here that when we use the term Balmer’s equation, Balmer in terms of emissions which means we’re going from a  higher shell number to a lower shell number, it usually means we’re starting off at a higher shell number and we’re going down to the second shell. That represents a Balmer emission. That deals with the origin of this equation.

When they were talking about Balmer’s equation, the final n final would’ve been 2. It doesn't necessarily always have to equal 2 now because they could give you a different value for the final shell number. Just realize that in the origins of this equation are 

n final = 2. This is because a Balmer emission is going from a higher shell number down to shell number 2, making shell number 2 our final shell. 

Summary

Remember that with Bohr’s equation and Balmer’s equation, they try to understand what’s happening to a photon as it goes from one shell to another. With Bohr’s equation, we’re relating shell numbers to energy. With the Balmer equation, we’re relating shell numbers to wavelength. 


Jules Bruno

Jules felt a void in his life after his English degree from Duke, so he started tutoring in 2007 and got a B.S. in Chemistry from FIU. He’s exceptionally skilled at making concepts dead simple and helping students in covalent bonds of knowledge.


When an electron of an excited hydrogen atom falls from level n = 3 to level n = 1, what is the frequency (in s-1) of the light emitted? a. 2.92 x1 0 15 b. 3.43 x 10 -16 c. 1.62 x 10 -15 d. 6.17 x 10 14 e. 4.00 x 10 19
How much energy is emitted in kJ/mol when an electron in the H atom transitions from n = 6 to n = 2? A. 275 B. 292 C. 302  D. 310 E. 321
 For a hydrogen atom, calculate the energy (in kJ) of a photon in the Balmer series that results from the transition n = 5 to n = 2. a. 1.09x10 -20 kJ b. 2.04x10 -21 kJ c. 2.18x10 -21 kJ d. 3.03x10 -22 kJ e. 4.58x10 -22 kJ
Atoms with one electron can be modeled with an equation similar to the Bohr equation:          Ea = -2.179x10-18 J (Z2/n2) In the equation, Z is the nuclear charge and n is the shell in which the electron resides. What is the ionization energy of Li2+, assuming its electron is originally in the n=1 level? A. 984.1 kJ/mol B. 1312 kJ/mol C. 495 kJ/mol D. 3937 kJ/mol E. 2953 kJ/mol  
What is the energy of the light emitted from a hydrogen atom as it relaxes from  the n = 5 to n = 3 excited states?                   What is the wavelength of the emitted light?    
How much energy is emitted in kJ/mol when an electron in the H atom transitions from n=6 to n=2? A. 275 B. 292 C 302 D. 310 E. 321
The electron in the  n = 5 level of a hydrogen atom emits a photon with a wavelength of 1280 nm. To what energy level does the electron move? 1. 5 2. 9 3. 8 4. 4 5. 6 6. 2 7. 7 8. 3 9. 1
A hydrogen atom initially in the n - 6 state emits a photon of ligiht of wavelength: λ = 1093 nm The value for n after emission of the photon is a. n = 1 b. n = 2 c. n = 3 d. n = 4 e. n = 5
The Rydberg equation is an empirical equation that describes mathematically 1. the lines in the emission spectrum of hydrogen. 2. the results of the cathode ray experiments. 3. the results of the oil drop experiment. 4. the Bohr model of the atom 5. the possible paths of two isotopes of the same element in a constant magnetic field in a mass spectrometer.
An electron in a hydrogen atom moves from the n = 2 to n = 5 level. What is the wavelength of the photon that corresponds to this transition and is the photon emitted or absorbed during this process? 1. 1875 nm; emitted 2. 434 nm; absorbed 3. 276 nm; emitted 4. 1875 nm; absorbed 5. 276 nm; absorbed 6. 434 nm; emitted 
It is possible to determine the ionization energy for hydrogen using the Bohr equation. Calculate the ionization energy (in kJ) for a mole of hydrogen atoms, making the assumption that ionization is the transition from n = 1 to n = ∞. A. 7.62 x 103 kJ B. 2.76 x 103 kJ C. 1.31 x 103 kJ D. 3.62 x 103 kJ E. 5.33 x 103 kJ
An atomic emission spectrum of hydrogen shows the following three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.For nm = 1875 { m nm}.
An atomic emission spectrum of hydrogen shows the following three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.For nm = 1093 { m nm}.
Calculate the wavelength of the radiation released when an electron moves from n = 6 to n =2.
With reference to the figure below, are the allowed energy states in the Bohr model for the H atom more like steps or more like a ramp?
How much energy does the electron have initially in the n = 4 excited state? Enter your answer numerically in joules.   What is the change in energy if the electron from Part A now drops to the ground state? Enter your answer numerically in joules.
For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition: (b) from n = 5 to n = 2
For each of the following electronic transitions in the hydrogen atom, calculate the energy, frequency, and wavelength of the associated radiation, and determine whether the radiation is emitted or absorbed during the transition: (c) from n = 3 to n= 6. Does any of these transitions emit or absorb visible light?
What is the wavelength of the light emitted from a hydrogen atom when an electron moves from the n = 6 to n = 2 energy level?R = 1.096776 x 107 m-1.A. 2.74 x 10-7 mB. 4.10 x 10-7 mC. 2.22 x 10-1 mD. 2.44 x 106 mE. 3.65 x 106 m
Calculate the wavelength of light associated with the transition from n=1 to n=3 in the hydrogen atom. A. 103 nm                 B. 155 nm                 C. 646 nm                 D. 971 nm                 E. 136 nm
An excited hydrogen atom emits a photon with a frequency of 1.141 x 10 14 Hz to reach the n = 4 state. From what state did the electron originate?  a) n=2 b) n=3 c) n=5 d) n=6 
Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from n = 6 to n = 1.
Using Bohr's equation for the energy levels of the electron in the hydrogen atom, determine the energy (J) of an electron in the n = 4 level.a) -5.45 x 10 -19b) -1.84 x 10 -29c) -1.36 x 10 -19d) +1.84 x 10 -29e) -7.34 x 1018
The n = 2 to n = 10 transition in the Bohr hydrogen atom corresponds to the __________ of a photon with a wavelength of __________nm. a) emission, 380 b) absorption, 380 c) absorption, 657 d) emission, 657 e) emission, 389
Solving the Rydberg equation for energy change gives ΔE = R∞hc [1/n12 - 1/n22] where the Rydberg constant R∞ for hydrogen-like atoms is 1.097 x 107 m-1 Z2, and Z is the atomic number. (a) Calculate the energies needed to remove an electron from the n = 2 state and the n = 6 state in the Li2+ ion. n = 2  ____ x 10___ J                n = 6  ____ x 10___ J (Enter your answer in scientific notation.) (b) What is the wavelength (in nm) of the emitted photon in a transition from n = 6 to n = 2? _____ nm
An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?
The second line of the Balmer series occurs at wavelength of 486.13 nm. To which transition can we attribute this line?a) n = 6 to n = 2b) n = 5 to n = 2c) n = 4 to n = 2d) n = 3 to n = 2e) it is to the n = 1 level
Consider a hydrogen atom in the ground state. What is the energy (in J) of its electron?     Now consider an excited-state hydrogen atom. What is the energy (in J) of the electron in the n = 3 level?       
Consider a hydrogen atom in the ground state. What is the energy of its electron?Now consider an excited- state hydrogen atom. What is the energy of the electron in the n=4 level?
A red laser pointer emits light with a wavelength of 650 nm. (c) The laser pointer emits light because electrons in the material are excited (by a battery) from their ground state to an upper excited state. When the electrons return to the ground state, they lose the excess energy in the form of 650 nm photons. What is the energy gap between the ground state and excited state in the laser material?
Suppose energy is delivered to atoms of fluorine, chlorine, bromine, and iodine sufficient to cause each atom’s outermost electron to jump to the n=7 state. Now imagine that these electrons return to the ground state, giving off light as they fall. Which gas will emit light of the highest frequency?1. iodine2. chlorine3. fluorine 4. bromine
A hydrogen atom emits light in an electronic transition going from n=4 to n=2 lower shell. 1.) What is the frequency of this light?  2.) What wavelength is this and what color will it appear to the eye?(R = 2.18x10 -18 J; h = 6.63 x 10 -34 J•sec; c = 3.00x10 8 m/sec;1 nm = 10 -9 m) 
An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.
An electron in the n = 6 level of the hydrogen atom relaxes to a lower energy level, emitting light of λ = 410 nm. { m ; m nmFind the principal level to which the electron relaxed.
In the top part of image below, the four lines in the H atom spectrum are due to transitions from a level for which ni > 2 to the nf = 2 level. What is the value of ni for the red line in the spectrum?
Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each of the following transitions.n = 5 → n = 1
A ground-state H atom absorbs a photon of wavelength 94.91 nm, and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 1281 nm to reach an intermediate energy level, and a second to return to the ground state. What higher level did the electron reach?
A ground-state H atom absorbs a photon of wavelength 94.91 nm, and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 1281 nm to reach an intermediate energy level, and a second to return to the ground state. What was the wavelength of the second photon emitted?
One of the visible lines in the hydrogen emission spectrum corresponds to the n=6 to n=2 electronic transition. What color light is this transition? Refer to the following figure.
Use the Rydberg equation to find the wavelength (in nm) of the photon emitted when an electron in an H atom undergoes a transition from n = 5 to n = 2.
Use the Rydberg equation to find the wavelength (in Å) of the photon absorbed when an electron in an H atom undergoes a transition from n = 1 to n = 3.
Calculate the wavelength of light emitted when the following transition occur in the hydrogen atom. n = 3 → n = 2What type of electromagnetic radiation is emitted?
Calculate the wavelength of light emitted when the following transition occur in the hydrogen atom. n = 4 → n = 2What type of electromagnetic radiation is emitted?
Calculate the wavelength of light emitted when the following transition occur in the hydrogen atom. n = 2 → n = 1What type of electromagnetic radiation is emitted?
Consider a large number of hydrogen atoms with electrons randomly distributed in the n = 1, 2, 3, and 4 orbits.How many different wavelengths of light are emitted by these atoms as the electrons fall into lower-energy orbitals?
Calculate the wavelength of light emitted when the following transition occur in the hydrogen atom. n = 5 → n = 4What type of electromagnetic radiation is emitted?
Calculate the wavelength of light emitted when the following transition occur in the hydrogen atom. n = 5 → n = 3What type of electromagnetic radiation is emitted?
Calculate the longest and shortest wavelengths of light emitted by electrons in the hydrogen atom that begin in the n = 6 state and then fall to states with smaller values of  n.
Determine the wavelength of the light absorbed when an electron in a hydrogen atom makes a transition from an orbital in the n = 2 level to an orbital in the n =7 level.
Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is 1460 nm. What is the initial excited state for the electron (n = ?)?
An excited hydrogen atom with an electron in the  n = 5 state emits light having a frequency of 6.90 x 1014 s-1. Determine the principal quantum level for the final state in this electronic transition.
X-ray diffractometers often use metals that have had their core electrons excited as a source of X rays. Consider the 2p → 1s transition for copper, which is called the Kα transition. Calculate the wavelength of X rays (in angstroms) given off by the Kα transition if the energy given off by a mole of copper atoms is 7.77 × 105 kJ . (Note that 1Å = 10-10 m)
You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. Is ΔE for this process positive or negative?
The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1 eV = 1.602 × 10–19 J. Using the Bohr model, determine the energy, in electron volts, of the photon produced when an electron in a hydrogen atom moves from the orbit with n = 5 to the orbit with n = 2. Show your calculations.
Using the Bohr model, determine the lowest possible energy, in joules, for the electron in the Li2+ ion.
Using the Bohr model, determine the energy of an electron with n = 8 in a hydrogen atom.
Consider a large number of hydrogen atoms with electrons randomly distributed in the n = 1, 2, 3, and 4 orbits.Calculate the lowest and highest energies of light produced by these atoms as the electrons fall into lower-energy orbitals?
The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation En = (n + 1/2)hν, where n is a quantum number with possible values of 1, 2, ..., and ν is the frequency of vibration. The vibration frequency of HCl is approximately 8.85 x 1013 s-18.85; imes ;10^{13} ;{ m{s}}^{ - 1}. Starting with a "stationary" molecule, what minimum energy is required to excite a vibration in HCl?
The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation En = (n + 1/2)hν, where n is a quantum number with possible values of 1, 2, ..., and ν is the frequency of vibration. The vibration frequency of HCl is approximately 8.85 x 1013 s-1. What wavelength of light is required to excite this vibration?
Why are the emission wavelengths for hydrogen and helium different? And why does the equation that relates to emission spectra to the energy levels differ for hydrogen and helium?
Using equation E= (hcRH)(1/n2) = (-2.1810-18J)(1/n2), calculate the energy of an electron in the hydrogen atom when n = 6.
For a hydrogen-like atom, classify these electron transitions by whether they result in the absorption or emission of light. n = 3 to n = 2 n = 3 to n = 5 n = 1 to n = 3n = 2 to n = 1Ignoring sign, which transition is associated with the greatest energy change? a. n = 2 to n = 1 b. n = 1 to n = 3 c. n = 3 to n = 5 d. n = 3 to n = 2
Calculate the energy of a photon emitted when an electron in a hydrogen atom relaxes from n = 5 to n = 3?
If a single electron in a hydrogen atom is in the excited n = 4 state and eventually relaxes to lower states, there are six possible emission or spectral lines.  How many of these lines are in the visible region of the EM spectrum?a.  1b. 2c. 3d. 4e. all of them
As the energy level of an orbit becomes more negative, does the electron experience a stronger or weaker attraction to the nucleus?
(a) How much energy is required to ionize hydrogen when it is in the ground state?eV(b) How much energy is required to ionize hydrogen when it is in the state for which n = 5?eV
One of the emission lines of the hydrogen atom has a wavelength of 93.8 nm. (b) Determine the initial and final values of n associated with this emission.
What wavelength of light will be required to remove an electron from the n = 3 shell of a hydrogen atom?
Calculate the energy, in joules, required to excite a hydrogen atom by causing an electronic transition from the n = 1 to the n = 4 principal energy level.a. 2.07 x 10-29 J b. 2.19 x 105 J c. 2.04 x 10-18 J d. 3.27 x 10-17 J e. 2.25 x 10-18 J
Calculate the energy (J) change associated with an electron transition from n = 2 ton = 5 in a Bohr hydrogen atom.A) 6.5 x 10-19B) 5.5 x 10-19C) 8.7 x 10-20D) 4.6 x 10-19E) 5.8 x 10-53
A hydrogen atom absorbs a photon with a wavelength of 397.1 nm, which excites the atom’s electron. Determine the electron’s initial quantum level if the transition results in a final quantum level of n = 7.a) n = 4b) n = 3c) n = 1d) n = 2e) n = 5
 What is the largest wavelength in the Balmer series?
What is the smallest wavelength in the Balmer's series?
What is the wavelength of the line corresponding to n=4 in the Balmer series?
What is the wavelength of the line corresponding to n=5 in the Balmer series?
Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 3 to n = 1 energy level, based on the Bohr theory. Use the equation En = -2.18 x 10 -18 J [(1/nf2)-(1/ni2)]a. 2.92 x 1015 s-1b. 3.56 x 1014 s-1c. 2.92 x 1014 s-1d. 1.17 x 1015 s-1
1/λ = R ((1/22)—(1/m2))R= 1.097*107 m-1If m=3, in what range are wavelengths calculated from the generalized formula shown above?a) microwave (1 to 10-4 m)b) infrared (10-3 to 7*10-7 m)c) visible (7*10-7 to 4*10-7 m)d) ultraviolet (4*10-7 to 10-8m)e) X rays (10-8 to 10-13 m)
1/λ = R ((1/22)—(1/m2))If m=1, in what range are the wavelengths calculated from the generalized formula shown above?R= 1.097*107 m-1a) microwave (1 to 10-4 m)b) infrared (10-3 to 7*10-7 m)c) visible (7*10-7 to 4*10-7 m)d) ultraviolet (4*10^-7 to 10-8 m)e) X rays (10-8 to 10-13 m)
What is the smallest value of n for which the wavelength of a Balmer series line is smaller than 400 nm, which is the lower limit for wavelengths in the visible spectrum?
What is the frequency in Hz of the photon released when a hydrogen atom undergoes a transition from the excited state where n = 2 to the state where n = 1?
An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?
What wavelength of light (in nm) if absorbed by a ground-state hydrogen atom could cause an electron to transition to n=3? 
What is the wavelength (in nm) of light emitted from a hydrogen atom when an electron falls from the n = 5 to n = 2 energy level?a. 780b. 656c. 486d. 434e. 308
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 level did the electron begin?
Calculate the wavelength of light emitted when the electron in the hydrogen atom undergoes a transition from level n4 to n3?
The electron in a ground-state H atom absorbs a photon of wavelength 97.20 nm. To what energy level does it move?
How much energy does the electron have initially in the n=4 excited state? Enter your answer numerically in joules.    What is the change in energy if the electron from Part A now drops to the ground state? Enter your answer numerically in joules.
What is the energy (in kJ) of one photon of the electronic transition from n = 6 to n = 3 in hydrogen atom? Show your work for credit. 
Consider an element that reaches its first excited state by absorption of 379.0 nm light.a) Determine the energy difference (kJ/mol) between the ground state and the first excited state.b) If the degeneracies of the two states for the element are g*/go = 1, determine N*/N_0 at 2090 Kc) By what percentage does N*/N_0 change if the temperature is raised by 20 K?d) What is N*/N_0 at 5970 K?
How much energy is required to ionize hydrogen: a. When it is in the ground state and b. When it is in the 2nd excited state with n = 3.
Calculate the wavelength of light emitted when the following transition occur in the hydrogen atom. n = 4 → n = 3What type of electromagnetic radiation is emitted?
Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom. Show your calculations.
Calculate the wavelength of light that would cause an electron to transition from  n = 1 to n = 3 in the hydrogen atom. A) 103 nm B) 136 nm C) 646 nm D) 155 nm E) 971 nm
Does a photon of visible light (λ ≈ 400 to 700 nm) have sufficient energy to excite an electron in a hydrogen atom from the n = 1 to the n = 5 energy state? From the n = 2 to the n = 6 energy state?
An atomic emission spectrum of hydrogen shows the following three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.For nm = 1282 { m nm}.
The Lyman series of emission lines of the hydrogen atom are those for which nf = 1.Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed.
An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 138 THz.What is the value of n for the level in which the electron originated? Express your answer as an integer.
An excited hydrogen atom emits light with a frequency of 2.34 x 1014 Hz to reach the energy level for which n = 3. In what principal quantum level did the electron begin? a. 2 b. 5 c. 4 d. 6 e. none of the above
What are the wavelengths, in nanometers, of the bright lines of the hydrogen emission spectrum corresponding to the transition: n = 5 to n = 2.
Enter your answer in the provided box.Recall Planck's constant equals 6.63 x 10-34 J • s and the speed of light is 3.00 x 108 m/s. Calculate the wavelength (in am) of a photon emitted by a hydrogen atom when its electron drops from the n = 4 state to the n = 2 state.
Calculate the energy released when an electron falls from the n = 8 energy level to the n = 1 energy level in a hydrogen atom. 
Calculate the wavelength (in nm) of a photon (emitted/absorbed) when an electron on hydrogen moves from the n = 6 to the n = 11 shell.
What is the wavelength of the photons emitted by hydrogen atoms when they undergo n = 3 to n = 2 transitions? In which region of the electromagnetic spectrum does this radiation occur? a. Ultraviolet b. Infrared c. Microwaves d. Visible
Calculate the energy released when an electron falls from the n = 8 energy level to the n = 1 energy level in a hydrogen atom. 
Calculate the wavelength of light produced if an electron moves from n = 5 state to n = 3 state of an electron in a hydrogen atom.Express your answer to three significant figures and include the appropriate units. 
An electron in the n = 5 level of an H atom emits a photon of wavelength 434.17 nm. To what energy level does the electron move?
Determine the energy change associated with the transition from n = 2 to n = 5 in the hydrogen atom.a. +3.76 x 10 -19 Jb. +6.54 x 10 -19 Jc. -1.53 x 10 -19 Jd. -2.18 x 10 -19 Je. +4.58 x 10 -19 J
Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (λlambda) in the atomic spectrum of hydrogen: 1/λ = R(1/m2 - 1/n2). In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.