PHYS 112 Lecture Notes - Lecture 61: Electronvolt, Photon

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7 Jun 2022

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Related Questions

Consider an harmonic oscillator with spring constant k and massm.
- Find the classical frequency of this oscillator as a function ofthe spring constant and m.

In quantum mechanics, the spectrum of possible energies for thisoscillator is given by: En = hf (n + 1/2) where n is a naturalnumber: n = 0, 1, 2, 3, ..., h is Planckâs constant and f is thefrequency.
- Find the ground state energy as a function of the spring constantand the mass.
- What is the difference of energy between the second excited stateand the ground state?
- Assume now that the oscillator carries a unit of charge, what isthe wavelength of the photon emitted as a function of k and m whenthe oscillator goes from the first excited state down to the groundstate?
- What is the wavelength of the emitted photon of the previousquestion if k = 10eV/ Â°A2, where Â°A denotes Angstrom and eV:electron volt. Is the emitted photon in the visible spectrum of ahuman eye?

thank you so much for any help!

Suppose we have reason to suspect that a certain quantum objecthasonly three quantum states. When we excite a collection ofsuchobjects we observe that they emit electromagnetic radiationofthree different energies: 0.9 eV (infrared), 1.9 eV (visible),and 2.8 eV (visible).

(a) Draw a possible energy-level diagram for one of thequantumobjects, which has three bound states. On the diagram,indicate thetransitions corresponding to the emitted photons, andcheck thatthe possible transitions produce the observed photons andnoothers. When you are sure that your energy-level diagramisconsistent with the observed photon energies, enter the energiesofeach level (K+U, which is negative). EnterALLlevels before submitting; all of the energies must be correctto beproperly scored. The energy K+U of theground state is -4eV.

eV = energy of highest level(2nd excited state)

eV = energy of next highestlevel (1st excited state)
-4 eV = energy of groundstate

(b) The material is now cooled down to a very low temperature,andthe photon detector stops detecting photon emissions. Next abeamof light with a continuous range of energies from infraredthroughultraviolet shines on the material, and the photondetectorobserves the beam of light after it passes through thematerial.What photon energies in this beam of light are observed tobesignificantly reduced in intensity ("dark absorptionlines")?
Energy of highest-energy dark line:

eV
Energy of lowest-energy dark line:

eV

(c) There exists another possible set of energy levels fortheseobjects which produces the same photon emission spectrum. Onanalternative energy-level diagram, different from the one you drew inpart(a), indicate the transitions corresponding to theemittedphotons, and check that the possible transitions producetheobserved photons and no others. When you are sure thatyouralternative energy-level diagram is consistent with theobservedphoton energies, enter the energies of each level(K+U,which is negative). Enter ALL levelsbeforesubmitting; all of the energies must be correct to beproperlyscored.

eV = energy of highest level(2nd excited state)

eV = energy of next highestlevel (1st excited state)
-4 eV = energy of groundstate

(d) For your second proposed energy-level scheme, whatphotonenergies would be observed to be significantly reduced inintensityin an absorption experiment ("dark absorption lines")?(Given thedifferences from part (b), you can see that anabsorptionmeasurement can be used to tell which of your twoenergy-levelschemes is correct.)
Energy of highest-energy dark line: eV
Energy of lowest-energy dark line: eV

Please use the links on the Experiment page on theserverto complete the questions below and submit themforgrading.

Please use the Bohr model simulator at MichiganStateUniversity to complete the table below:

initial orbital	ending orbital	Wavelength (nm)
3	2
4	2
	2	434
	2	410.2
7	2	397
4	3
5	3

See the spectrum of any element at http://jersey.uoregon.edu/vlab/elements/Elements.html

Bohr Model Simulation McGraw-Hill (Java)

Explore :LightEmission and Absorption Tutorial(NortonPublishing)

Explore :BohrModelof the Atom Tutorial (Norton Publishing)

Hydrogen Line Spectrum Quicktime Movie (1M)McGraw-Hill

You can generate your own spectra with the MiniSpectroscopyJavaApplet

Line Spectrum Flash Tutorial

1. What is the job of a spectroscope?

2. Why is the helium spectrum have so many morelinesthan the hydrogen spectrum?

3. Would you expect the spectrum of He⁺ tobehave as many lines as the spectrum of He? Please explainyouranswer? (He⁺ is the ion formed when Helosesone electron.t

4. The H₂⁺ ion has onlyoneelectron. Would the spectrum of the H₂⁺ionresemble the spectrum for any of the following:H₂, H,He⁺, He? Please explainyour answer.

5. Which of the following can be expected to giveaspectrum most closely like that of the H atom: Li,Li⁺,Li⁺² ?

6. Spectrum wavelengths are sometimes measuredinAngstrom units. Please convert 675 nm to Angstroms. (1Angstrom =10^-10 meters. 1 nm =10^-9meters.)

7. If an electron is in energy level 4, whatdifferentwavelengths can it make in coming back to energy level 2.(Please remember that the fall down is not always done in justonedrop.)

8. An electron which falls all the way down toenergylevel 1 would give off much more energetic light. Whyweretransitions which ended at energy level 1 were not studied bytheunaided eye?

PHYS 112 Lecture Notes - Lecture 61: Electronvolt, Photon

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