Activity – Blackbody Radiation and the Ultraviolet Catastrophe
Introduction: A blackbody is a term used to describe the light given by an object that only gives off emitted light, in other words it doesn’t reflect light. Of course, in order for such an object to emit light it must get hot. In this activity, you are going to observe the nature of light given off by hot objects and determine if there is an empirical relationship between an object’s temperature and the light emitted.
These are some helpful video links which provide an excellent foundation of knowledge of Blackbody Radiation.
Crash Course (First Half of Video) https://www.youtube.com/watch?v=7kb1VT0J3DE&list=PL8dPuuaLjXtN0ge7yDk_UA0ldZJdhwkoV&index=44&t=438 s
Professor Dave’s Summary on Blackbody Radiation and the Ultraviolet Catastrophe https://www.youtube.com/watch?v=7BXvc9W97iU
PHET’s Manipulative Graph of Spectral Power Density vs. Wavelength https://phet.colorado.edu/en/simulation/blackbody-spectrum
Draw a graph depicting classical blackbody radiation, (Y-axis is Spectral Power Density, X-axis is Wavelength). Complete the graph correlating the spectral power density to wavelength for the sun, as demonstrated on the Phet activity.
Describe the correlation between wavelength of light emitted with the average kinetic energy of particles within a substance.
Temperature in Kelvin for Red Light:
Temperature in Kelvin for Yellow Light:
Temperature in Kelvin for Violet Light:
Questions:
Dianna Cowern with PBS has an enthusiastic video explaining the origin of quantum topics. https://www.youtube.com/watch?v=FXfrncRey-4
What does the ultraviolet catastrophe refer to, and why does the curve collapse on the left-hand side of the graph? (At what approximate wavelength does the curve drop)?
What is Max Planck’s explanation for the ultraviolet catastrophe, and how does it lead to the Planck equation? (Provide Planck equation and Planck’s constant).
Activity – Atomic Spectra Practice
We don’t watch a lot of Khan Academy videos, but the below video links do provide a modest foundation for spectral analysis, and electron movement within atomic shells.
Khan Academy Videos: https://www.khanacademy.org/science/physics/quantum-physics/atoms-and-electrons/v/atomic-energy-levels https://www.khanacademy.org/science/physics/quantum-physics/atoms-and-electrons/v/bohr-model-energy-levels
EEmitted Photon = (EHigher Level – ELower Level)
1 eV = 1.6 X 10-19 Joules
Bohr’s Conclusions:
(1) Electrons don’t lose energy as they accelerate around the nucleus. Instead energy is quantized. Electrons can only exist at specific discrete energy levels. These energy levels are given by the following equation, where Z is the atomic number and n is the positive integer energy level:
Z = Atomic Number n = Energy Level
(2) Each atom allows only a limited number of specific orbits, (electrons), at each energy level.
(3) To change energy levels, an electron must absorb or emit a photon of energy exactly equal to the difference between the electron’s initial and final energy levels.
EPhoton = EInitial – EFinal
To Find Properties About an Emitted Electron:
EnergyTotal = EnergyBinding – EnergyElectron Retains After Emission
The accompanying 13 practice problems are a terrific way to start building familiarity with energy-level diagram problems for electron movement in orbital shells.
Use the below information to answer Questions 1 – 2. The first five energy levels of an atom are shown in the diagram below:
(1) If the atom begins in the n = 3 level, what photon energies could be emitted as it returns to its ground state?
(2) What could happen if this atom, while in an undetermined energy state, were bombarded with a photon of energy equals 10 eV?
Use the below information to answer Questions 3 – 4.
(3) Using the energy level in the diagram for hydrogen above, how much energy must a ground-state electron in a hydrogen atom absorb to be excited to the n = 4 energy level?
(4) With the electron in the n = 4 level, what wavelengths are possible for the photon emitted when the electron drops to a lower energy level? In what regions of the electromagnetic spectrum do these photons lie?
Use the below information to answer Questions 5 – 6. A hypothetical atom has two energy levels, as shown below.
(5) What wavelengths of electromagnetic radiation can be absorbed by this atom?
(6) Now, monochromatic 180 nm ultraviolet radiation is incident on the atom, ejecting an electron from the ground state. What will be --
•The ejected electron’s kinetic energy •The ejected electron’s speed •The incident photon’s speed
Use the below energy level diagram of hydrogen to answer Questions 7 – 11.
(7) An electron in a hydrogen atom drops from the n = 3 to the n = 2 state. Determine the energy of the emitted radiation.
(8) Which type of photon is emitted when an electron in a hydrogen atom drops from the n = 2 to the n = 1 energy level?
(9) Determine the energy, in eV, of a photon emitted by an electron as it moves from the n = 6 to the n = 2 energy level in a hydrogen atom.
(10) Convert the energy of the photon to Joules.
(11) Calculate the frequency of the emitted photon.
Use the below energy level diagram for mercury to answer Questions 12 – 13.
(12) An electron in a mercury atom drops from energy level “f” to energy level “c” by emitting a photon having an energy of --
(13) A mercury atom in the ground state absorbs 20 eV of energy and is ionized by losing an electron. How much kinetic energy does this electron have after the ionization?
Answers:
(1) 55 eV (7) 1.89 eV (2) No two energy levels are separated by 10 eV; nothing happens (8) 1.22 X 10-7 m; 2.46 X 1015 Hz (3) + 12.75 eV (4) (9) 3.02 eV 4 3 0.65 eV; 1.91 X 10-6 m; 1.57 X 1014 Hz (10) 4.83 X 10-19 J
4 2 (11) 7.29 X 1014 Hz 2.55 eV; 4.87 X 10-7 m; 6.16 X 1014 Hz (12) 2.84 eV 4 1 12.8 eV; 9.71 X 10-8 m; 4.1 X 1015 Hz (13) 9.62 eV
(5) All possible combinations in which e- move to a higher state -7 14 ΔE12 = 2.1 eV; 5.92 X 10 m; 5.07 X 10 Hz -7 14 ΔE1Infinity = 3.3 eV; 3.76 X 10 m; 7.97 X 10 Hz (Ionized from Shell # 1) -7 14 ΔE2Infinity = 1.2 eV; 1.04 X 10 m; 2.89 X 10 Hz (Ionized from Shell # 1)
(6) First, find energy of incident light. The residual energy will characterize the electron after ionization. (Photon velocity always equals 3.0 X 108 m/s).
Frequency = 1.667 X 1015 Hz
Energy = 6.9 eV; Residual Energy = 3.6 eV
Convert Residual Energy to Joules, then use the definition of kinetic energy to determine electron velocity; 1.1 X 106 m/s
Lab Activity - Spectral Analysis of Hydrogen
This is a sample laboratory activity which makes use of the theory investigated in Spectral Analysis – Practice (Day Four), in order to investigate hydrogen gas’s spectral map.
First, let’s catch a couple of video links which provide a foundation of knowledge which will help us interpret lab results.
Firstly, there’s a pretty simple video which lays out the procedure for basic spectral analysis. Then, Paul Andersen’s summary video of spectral analysis does a great job of simplifying the steps involved in competent spectral analysis. https://www.youtube.com/watch?v=nM5Kg7RUoTE https://www.youtube.com/watch?v=1uPyq63aRvg
We will perform a laboratory which will make use of hydrogen’s spectral pattern to map hydrogen’s energy-level diagram. (Actually, I’ll give you the data I’ve observed when performing this procedure, unless you’ve got a spectral scope and a set of element-specific discharge tubes at home).
Claim: Explain the procedure we will use to map the energy-level diagram for hydrogen. Include in your explanation: •Diagram of Experimental Setup, including: ►Glass-Discharge Chamber ►Spectrometer ►Formation of Bands Within Spectrometer
•Explain why there are so many energy levels for the hydrogen atom, even though it has one orbital shell, according to chemistry definitions of hydrogen’s orbital structure
Include in your description of this experiment the following items: •Why introducing a high-voltage to the gas within the glass tube causes it to glow at specific wavelengths •Explanation and diagram of all variables within the below equation, (including Rydberg constant)
Which series are visible/invisible, and what energy-level jumps are indicated by each series? •Lyman Series •Balmer Series •Paschen Series
•What formulas and calculations are necessary to correlate wavelength to energy associated with electron energy- level drop?
Evidence: First, record the wavelength and color of each band formed. Then, calculate the energy-level associated with that jump. Using this information, along with our understanding of the series indicated, provide an energy-level diagram for hydrogen, such that each energy-level jump indicates the wavelength and energy amount. ______
(Looking through the spectroscope, we encounter the below spectral lines).
(Remember, the spectral lines we encounter are indicative of the Balmer series, those of the visible light spectrum). (No need for a justification section).