Atomic Structure and Light

Background Material

Carefully read all the material under the links in the Hydrogen Energy Levels NAAP website lab, then answer the following questions.

1. Complete the following table which relates the properties of two different photons by highlighting in blue the appropriate relationship. The first row is completed for you: "A red photon has a longer wavelength, lower frequency, less energy, and the same velocity through space as a blue photon".

Photon A	Wavelength	Frequency	Energy	Velocity (in space)	Photon B
Red	longer the same shorter	higher the same lower	more the same less	larger the same smaller	Blue
Orange	longer the same shorter	higher the same lower	more the same less	larger the same smaller	Red
Infrared	longer the same shorter	higher the same lower	more the same less	larger the same smaller	Radio
Visual	longer the same shorter	higher the same lower	more the same less	larger the same smaller	Microwave
Gamma ray	longer the same shorter	higher the same lower	more the same less	larger the same smaller	X-ray

2. Scientists often say "A is proportional to B" if B increases when A increases. They also say "A is inversely proportional to C" if C decreases when A increases. Inspect the table above for evidence of such relationships and use these terms (proportional or inversely proportional) to describe the relationships between wavelength and frequency; wavelength and energy; and frequency and energy.

Hydrogen Atom Simulator - Introduction

The Hydrogen Atom Simulator allows you to view the interaction of an idealized Hydrogen atom with photons of various wavelengths. Assume this atom is far from the influence of neighboring atoms and is not moving. The simulator consists of four panels. Below gives a brief overview of the basics of the simulator.

• The panel in the upper left shows the Bohr Model: the proton, electron, and the first six orbitals with the correct relative spacing.
  • The electron can absorb a photon and jump to a higher energy level, where it will remain for a short time before it emits a photon(s) and drops to a lower energy.
  • The electron can also be ionized (removed from the atom). If this occurs, the simulator will cause the atom to absorb an electron a short time later.
  • For convenience you can drag the electron between levels. Once it is released it will behave "physically", as if it had gotten to that present level without being dragged.
• The upper right panel labeled "energy level diagram" shows the energy levels vertically with correct relative spacing.
• The "Photon Selection" panel (bottom left) allows you to "shoot" photons at the Hydrogen atom. The slider allows the user to pick a photon of a particular energy/wavelength/frequency.
  • Note how energy and frequency are directly proportional and energy and wavelength are inversely proportional.
  • On the slider are some of the energies which correspond to levels in the Lyman (UV), Balmer (Visible), and Paschen (Infrared) series.
  • Clicking on the label will shoot a photon of that energy.
  • If the photon is in the visual band, its true color is shown. Photons of wavelengths longer than visible are shown as red, and wavelengths shorter than visible are shown as violet.
• The "Event Log" in the lower right lists all the photons that the atom has encountered as well as all the electron transitions.
• The log can be cleared by either using the button or manually dragging the electron to a particular energy level.

Hydrogen Atom Simulator - Exercises

For any particular level of the Hydrogen atom, you can think of the photons that interact with it as belonging to one of three groups:

Increasing Energy
Range 1 None of the photons have enough energy to affect the atom.	Range 2 Some of the photons have the right energy to make the electrons to jump to a higher energy level (i.e. excite them).	Range 3 All the photons have enough energy to ionize the atom.

Note that the ranges are different for each energy level. Below is an example of the ranges for an electron in the ground state of a Hydrogen atom.

Ground State electron of H
Range 1 0eV to 10.2 eV (10.2 eV needed to excite electron to 2nd energy level)	Range 2 10.2 to 13.6 (some will excite, some won't)	Range 3 >13.6 eV (anything greater than this will ionize the atom)

When the simulator first loads, the electron is in the ground state and the slider is at 271 nm.

• Fire a 271 nm photon. This photon is in range 1.
• Gradually increase the slider to find a photon which is in range 2. The first photon in this range will be the Lyman- line (which is the energy difference between the ground state and the second energy level).
• Increase the energy a bit more from the Lyman- line and click "fire photon". Note that nothing happens. This is a range 2 photon but it doesn't have the "right energy".
• Increase the energy more until photons of range 3 are reached. In the simulator this will be just above the L line.
  • Technically there are photons which would excite to the 7^th, 8^th, 9^th, etc. energy levels, but these are very close together and those lines not shown on the simulator.
  • The L line has an energy of -13.22 eV and is in range two. The ionization energy for an electron in the ground state is 13.6 eV, so that is the correct range 3 boundary.

1. Which photons will excite the Hydrogen atom when its electron is in the ground state? You can list the photon names or energies (in eV).

1. Which photons will further excite (but not ionize) the Hydrogen atom when its electron is in the second energy level? You can list the photon names or energies.
3. Complete the energy range values for the 1^st excited state (when the electron is in the second energy level) of Hydrogen. Use the simulator to fill out ranges 2 and 3. The electron can be placed in the 2^nd level by manually dragging the electron or firing a L photon once when the electron is in the ground state. Note also that the electron will deexcite with time, so you may need to place it in the 2^nd level repeatedly.

1st Excited State Electron in H
Range 1 0 to 1.9 eV (anything less than this energy will fail to excite the atom)	Range 2	Range 3

2. What is the necessary condition within a Hydrogen atom for Balmer photons (H, H_, etc) to be absorbed by the atom without causing ionization?

1. An ultraviolet photon is produced whenever the electron within a Hydrogen atom transitions from a higher energy level down to the ground state, which produces the Lyman lines. Why do these Lyman transitions produce ultraviolet photons, while theBalmer transitions produce visible light photons?

1. Starting from the ground state, there are two paths an electron can take to get to the 6^th energy level with only two transitions. One path is illustrated below in Method 1. In the energy level diagram under Method 2, use the Arrow Tool (under Shapes, found under the Insert tab in Word) to illustrate the other possible path to the 6^th orbital, with just two transitions. In the boxes to the left of the Method 2 diagram, label each transition with the name of the photon used.

a) Method 1:

b) Method 2:

1. Usethree different photons to bring the electron from the ground state to the 4^th energy level. Use the Arrow Tool to illustrate your transitions with arrows ontheenergy level diagram. In the boxes to the right of the diagram, label each transition with the name of the photon used.

1. How does the energy of a photon emitted when the electron moves from the 3^rd to the 2^nd energy level compare to the energy of a photon absorbed when the electron moves from the 2^nd to the 3^rd energy level? Explain.
6. Determine the amount of energy needed for the following 3 transitions.

• Level 1 to Level 2
• Level 2 to Level 3
• Level 3 to Level 4

1. Explain why these transitions require different energy levels.

Summary/Conclusion (5 points): The identification of absorption or emission lines in the light spectrum of a distant object is the only way we can identify elements in that object. Give a detailed explanation of what is happening within the hydrogen atom to create emission lines. Why do we see absorption lines instead of emission lines when we look at the spectra of stars?