## Kinesthetic Model of Discrete Spectra

**Overview:** Students represent the spectrum of Cas A in both "rainbow" and plot forms, learn about the quantum mechanics of discrete spectrum generation, and participate in a kinesthetic model where they take on the role of electrons which "jump" from energy level to energy level in different elements.

**Physical resources:** Diffraction gratings, incandescent light bulb, emission tubes, masking tape, colored candies, graph paper

**Electronic resources:** Spectrum Explorer, Physics 2000 article on spectrum lines

**Observing discrete spectra and atomic structure**

- Instructor shows students how to use a diffraction grating to observe an incandescent light bulb and different emission tube spectra. (Emission tubes have one vaporized element, and so show only discrete spectral lines.)(diffraction incandescent, diffraction emission)
- Students are challenged to use Project LITE Spectrum Explorer "drawing" tool to reproduce the two spectra they saw from the two sources. (Allowing them to refresh their understanding of the relationship between projected spectra and how they are represented in histograms.)
- Focus questions (for notebook writing, after observations):
- How was the incandescent light bulb spectrum similar to the neutron star spectrum from investigation 3? (Shows all the colors, continuously.)
- How was the hydrogen spectrum similar to the supernova remnant spectrum we saw for Cas A? (Shows only discrete colors.)

- Reading about discrete spectra: Physics 2000 material: (Spectrum lines)
- Read through 4 screens, playing with each applet.
- Students record the 2 most important things they learned from this reading (takes about 30 minutes) and share with their group.
- Typical responses: Electrons are only allowed in orbitals with certain energies, elements each have their own unique "signature" spectrum of lines, etc.

**Kinesthetic atomic line spectrum production simulation**

- Students will become electrons orbiting different atoms of the same element. We
**won't**represent them moving in their orbitals, but instead represent the energy that each electron has. - Preparation:
- Put tape on the floor to represent energy levels of atoms of two different elements: (energy levels 1, energy levels 2)
- Shakibium, with electron energy levels: 1 eV, 3 eV and 4 eV
- Peterium, with electron energy levels 0.5 eV, 3.0 eV and 4.5 eV

- Code colored chocolate candies by energy: 1 eV = red, 1.5 eV = pink, 2 eV = yellow, 2.5 eV = orange, 3 eV = brown, 3.5 eV = green, 4.0 eV = blue
- Each student begins with an assortment of colored candies.

- Put tape on the floor to represent energy levels of atoms of two different elements: (energy levels 1, energy levels 2)
- Stages of model:
- Each student represents an electron in orbit around one atom of the gas "Shakibium", so the entire group is a "box of gas".
- All electrons are in the lowest energy state, so stand on the line representing this lowest energy electron state.
- Instructor somehow "adds energy" to the gas: this could be heating it up, or adding electrical energy, or simply waiting for thermal motion to excite some of the atoms in the box through collisions.
- Each student "decides" how much energy they have gained, and so "jump" to a higher level.
- Time passes, and each student then "decides" which lower level to "fall" to. (Does not have to be the lowest state just yet.)
- That student then "emits" a photon with the energy equal to the difference in the energy levels they've just transferred between. Instructor collects these photons.
- More time passes, and all students eventually "fall" back to the lowest state. (Some students will have to emit two photons, if they fall to the intermediate state first.)

- Repeat this process several times, to build up "sets" of photons. Small groups of students then make a histogram of the energy spectrum they've released.
- After one element is understood, have at least some students instead represent atoms of Peterium. Students repeat the process above, including making a histogram for the second element: (kinesthetic spectra).
- Focus question: Why are there differences between the spectra emitted by these two boxes of gas? (i.e. there are differences in the spacing of the electron energy levels in the two kinds of atoms.)

**Teacher tips/tricks:**

- Students may see differences in the heights of the peaks in the elements' spectra, because the students get to arbitrarily "choose" which energy levels to "jump" and "fall" to. In reality, quantum mechanical models of different atoms predict the probability for what energy levels a particular electron will inhabit, and thus the number of transitions one would expect in a bunch of atoms. Thus, the important difference here to emphasize is the different (and unique) energy of photons which are emitted by each element.
- In the discussion of the focus question, have students try to relate their observations of the model to what they learned in the reading selection, in particular, their "two most important" things learned from the reading.
- Many students will refer to the "energy level" of a photon, meaning that it has a certain energy. However, this is confusing when both electrons
**and**photons "have" an energy, as in this situation, so refer to "electron energy levels" but just "photon energy" or "energy of a photon".

**Assessment ideas:**

- Ask students to write what each of the parts of the model represent in reality: each student (electron in "orbit" around one atom), chocolate candy (photons), tape on the floor (electron energy levels). What is
**not**represented in this model? (the motion of the electron around the atom, thermal motion of atoms, etc.). - Ask students to discuss and write their answer: Why was the spectrum of Shakibium different from the spectrum from Peterium?