IIT/FIELD MUSEUM – High School Transformation Project

Lesson: Planck’s law and fluorescence

Hewitt Ch. 38, sections 38.1-38.4

This is also aligned to PSAE 13.11.05 and 13.11.09

  • Guiding questions

How is a photon’s energy related to its frequency (color)?

What causes fluorescent bio-molecules to glow?

  • Context of Lesson

This lesson will reference students’ prior knowledge and experiences with light, energy, and the atomic model of matter. A more involved treatment of quanta could follow this lesson. Students should have had some experience with the wave equation and energy as a function of frequency (for example, the frequency of sunlight with the highest intensity is yellow-green, which is why it is used on safety vests, etc.).

  • Main Goals/ Objectives:

By the end of this lesson, students will be able to understand Planck’s law, and be able to explain the particle nature of light in general terms. Students will make inferences as to the applications of these phenomena to biotechnology applications, specifically for the purpose of identification of particular strains of bacteria.

Nature of Science: Integrated Theme

2. Explain that scientists’ creativity influence their doing inquiry so they may have different observations and interpretations of the same phenomena.

3. Distinguish observations from inferences, explain that inferences should be based on observations, and explain that the development of scientific knowledge involves both observations and inferences so scientific knowledge is partially inferential.
7. Explain that scientific knowledge should be based on empirical data.

Scientific Inquiry: Integrated Theme

1. Explain that scientific investigations all begin with a question, but do not necessarily test a hypothesis.
3. Explain that inquiry procedures are guided by the question asked.
6. Explain that research conclusions must be consistent with the data collected.
8. Explain that explanations are developed from a combination of collected data and what is already known.

  • General Alignment to Standards

11A. Know and apply the concepts, principles and processes of scientific inquiry.

ILS 11.A.4b Conduct controlled experiments or simulations to test hypotheses

ILS 11.A.4c Collect, organize and analyze data accurately and precisely

12C. Know and apply concepts that describe properties of matter and energy and the interactions between them.

ILS 12.C.4a Use kinetic theory, wave theory, quantum theory, and the laws of thermodynamics to explain energy transformations.

PSAE STANDARD 11A – SCIENTIFIC INQUIRY

  • 11.11.01 Understand and follow procedures relating to scientific investigations, including understanding the design and procedures used to test a hypothesis, organizing and analyzing data accurately and precisely, producing and interpreting data tables and graphs, performing appropriate calculations, applying basic statistical methods to the data, identifying appropriate conclusions, making predictions, and evaluating competing models.
  • 11.11.02 Distinguish among the following: observing, drawing a conclusion based on observation, forming a hypothesis, conducting an experiment, organizing data, comparing data.

PSAE STANDARD 11B – TECHNOLOGICAL DESIGN

  • 11.11.07 Given test results on different models, choose the model which best solves the design problem.

PSAE STANDARD 12C – LIGHT AND SOUND

  • 12.11.91Understand that incoming solar radiation is either reflected or absorbed.

Materials

Each group will need the following:

Set of 5 LEDs

9 V battery with connector

1 kΩ potentiometer

330 Ω resistor

connecting lead

breadboard

voltmeter

Modifications/Accommodations:

  • This is a good lab for making groups from students with varying English language abilities because the lab is data-oriented and hands-on.
  • This is a visual lab. There is a color component that may be difficult for some learners with visual impairments.
  • With more time, it is simple to extend this lab to a second day with the addition of diverging lenses.

The Lesson:

Bell Ringer:

What is a photon and how much energy does it have?

In 1900, Max Planck asked: “How is the temperature of an object related to the frequency of electromagnetic radiation it emits?” His work only made sense if he assumed that the energy of a vibrating molecule was quantized—this means it could only take on certain values. The energy would have to be proportional to the frequency of vibration, and it seemed to come in little "packets" of the frequency multiplied by a certain constant. This constant came to be known as Planck's constant, (symbol h). h = 6.626 x 10 -34 Joule●seconds, an incredibly small number!
At the time (and even today) it was somewhat outlandish to suggest that energy could only come in discrete amounts. Planck actually didn't realize how revolutionary his work was.

Discussion:

Based on Planck's work, Einstein proposed that light also delivers its energy in chunks; light would then consist of little particles, or quanta, called photons, each with an energy of Planck's constant times its frequency. This means that higher-frequency photons have more energy, which, when striking certain atoms, emits faster electrons (this is the Photoelectric Effect). If you keep the brightness of a light the same but increase the frequency (change the color) the maximum kinetic energy of the emitted electrons should increase also. If you only increase the brightness of a light hitting atoms, more electrons should be emitted (because there are more photons to hit them), but they won't come out any faster, because each individual photon still has the same kinetic energy. Likewise, if the frequency is low enough, then none of the photons will have enough energy for an atom to emit an electron. So if you bombard atoms with really low-frequency light, these atoms shouldn't emit any electrons, no matter how bright that light is.

The photoelectric effect was able to tell us whether light is in fact made up of particles or waves. In 1913-1914, Robert Millikan did a series of extremely careful experiments involving the photoelectric effect. He found that all of his results agreed exactly with Einstein's predictions about photons, not with the wave theory. Einstein actually won the Nobel Prize in 1921 for his work on the photoelectric effect. So light has characteristics of particles and, based on experiments such as diffraction, it also has characteristics of waves. It has a dual nature, and can behave as a wave or a particle, depending on what methods of detection are used.

For atoms involved in fluorescence, when an atomic electron receives enough energy to ‘jump” to a higher energy level, it then releases that energy in the form of a photon (electromagnetic radiation), except that the photon has less energy than the original input energy because some energy is dissipated (as internal energy when the molecule undergoes changes in conformation).

Molecules that glow in the dark contain atoms or groups of atoms called fluorophores. Fluorophores can be naturally occurring or can be synthesized. Examples of naturally occurring fluorophores are quinine, (the first fluorophore to be discovered), and Green Fluorescent Protein (GFP) and Blue fluorescent Protein (BFP) from jellyfish.

In this experiment the energy required to just barely light an LED is compared to the frequency (color) of photons emitted by that LED. The experiment is based on this principle: the energy lost by a single electron that passes through a light-emitting diode (LED) is converted into the energy of one photon. We are interested in measuring the energy required to make the LED just barely visible, rather than bright. The reason for this is because when the LED is bright, not all the electric energy can be assumed to be converted to photons of visible light (dissipated energy is significant for brightly lit LEDs).

Materials

Set of 5 LEDs

9 V battery with connector

1 kΩ potentiometer

330 Ω resistor

connecting lead

breadboard

voltmeter

Procedure

1. Set up a table to record voltage vs. wavelength for each of the five LEDs.

2. Orient the potentiometer so that the terminals are pointing towards you and turn the knob fully clockwise. As shown in Figure 1, check that the negative terminal of the battery is connected to the left-hand terminal of the potentiometer. Check that the positive terminal of the battery is connected to the right-hand terminal of the potentiometer. Check that the resistor is connected to the middle terminal of the potentiometer.

3. Check that the short end (without the colored flag) of one of the LEDs is connected to the 330 Ω resistor on the breadboard as shown in Figure 2.

4. Clip a wire from the positive terminal of the potentiometer to the longer (flagged) wire of the LED. See figure 2.

5. Have your partner hold the leads of the voltmeter so that it measures voltage across the LED as shown in figure 3.

6. Slowly increase the potential difference across the LED by turning the potentiometer knob counterclockwise until the LED just begins to glow. Record the potential difference at which this happens. Go backwards and forwards past the point at which the LED just begins to glow a few times to locate it as accurately as possible, and use a viewing tube to verify your impressions.

7. Turn the potentiometer knob fully clockwise so the voltage is 0V and disconnect the LED. Repeat Steps 5 and 6 for all the other LEDs.

Homework

Written defense of laboratory results

Hewitt ch. 38check concepts 1- 7

Assessment:

This lab should be assessed with a broad range of criteria, including group participation, written work, and knowledge gained.

Walk around the room during the bell-ringer activity. See which groups are working together effectively, and which groups are having difficulty. Re-check groups having difficulty to confirm that they are making progress.

Students can turn in their completed data table on the day for data collection. This can serve as an assessment for their ability to properly collect and organize data as they continue with the investigation.

Name:______per:______date:______

Planck’s Law and Fluorescence – Day 1

NOTE: The wavelengths of the LEDs: violet= 420 nm, blue = 470 nm, green = 524 nm, orange = 605 nm, red = 631 nm.

Some basic quantities are

e = elementary charge = 1.6 x 10-19 C

Velocity of light = c = 3x108 m/s

ΔV = potential difference across LED

f = frequency of a photon emitted by LED

1. Convert Voltage into Energy, and Wavelength into Frequency by entering into the white columns of the spreadsheet below your measured voltage (in Volts = Joules/Coulomb) and wavelength (in nanometers).

Calculate Frequency using:

f = =

Calculate Energy of each photon using:

E = Voltage (in Joules/Coulomb) x 1.6 x 10 -19 Coulombs / electron

Remember, the energy lost by a single electron that passes through a light-emitting diode (LED) is converted into the energy of one photon.

2. Make a graph of Energy (vertical axis) vs. Frequency.

Conclusion and Discussion

  1. Draw a Best Fit line. Calculate the slope and write the equation for this line.
  1. What is the meaning of the slope of this line? How does it compare to the accepted value of Planck’s constant?
  1. Does the intercept have meaning? Explain.
  1. What are some assumptions that you must make about the data you collected?
  1. What are some sources of experimental error and how could these errors be minimized?
  1. What is the percentage error in your calculated value for Planck’s Constant?

Practice Problems

The excitation spectrum (left curve) of native GFP from jellyfish has two excitation maxima: at 395 nm and at 470 nm.

The fluorescence emissionspectrum (right curve) has a peak at 509 nm and a shoulder at 540 nm.

1. A. Calculate the energy of the photons that are absorbed and emitted by green fluorescent protein, based on the diagram above.

B. Which frequency in question 1 has the most energy?

C. Using your knowledge of the electromagnetic spectrum, is this electromagnetic radiation visible to humans? Explain.

2. An ultraviolet light source has irradiance of 2 Watts/cm2. If this light shines on 1 square centimeter of bacterial cells on a Petri plate for 10 minutes, how many Joules of energy is this. If the light has a wavelength of 365 nm, how many photons of UV is this?

Name:______Key______per:______date:______

Planck’s Law and Fluorescence – Day 1

NOTE: The wavelengths of the LEDs: violet= 420 nm, blue = 470 nm, green = 524 nm, orange = 605 nm, red = 631 nm.

Some basic quantities are

e = elementary charge = 1.6 x 10-19 C

Velocity of light = c = 3x108 m/s

ΔV = potential difference across LED

f = frequency of a photon emitted by LED

1. Convert Voltage into Energy, and Wavelength into Frequency by entering into the white columns of the spreadsheet below your measured voltage (in Volts = Joules/Coulomb) and wavelength (in nanometers).

Calculate Frequency using:

f = =

violet : 3 x 108 / 4.2 x 10-7 = 7.1 x 1014 Hz

blue : 3 x 108 / 4.7 x 10-7 = 6.4 x 1014 Hz

green : 3 x 108 / 5.24 x 10-7 = 5.72 x 1014 Hz

orange : 3 x 108 / 6.05 x 10-7 = 4.96 x 1014 Hz

red : 3 x 108 / 6.31 x 10-7 = 4.75 x 1014 Hz

Calculate Energy of each photon using:

E = Voltage (in Joules/Coulomb) x 1.6 x 10 -19 Coulombs / electron

Values will be based on data collected by students.

Remember, the energy lost by a single electron that passes through a light-emitting diode (LED) is converted into the energy of one photon.

2. Make a graph of Energy (vertical axis) vs. Frequency.

Conclusion and Discussion

  1. Draw a Best Fit line. Calculate the slope and write the equation for this line.

The slope is 6.63 x 10-34 J-s.

  1. What is the meaning of the slope of this line?

The slope will be Planck’s constant, from E = hf.

  1. Does the intercept have meaning? Explain.

What appears to be the y-intercept is the minimum energy required to produce visible light. If the graph were to be extended to include all of the electromagnetic spectrum, it would start at the origin, according to E = hf.

  1. What are some assumptions that you must make about the data you collected?

a. All of the electrical energy is converted to visible light.

b. No heat is produced – the system is 100% efficient.

c. The light that is produced is composed discretely of the respective wavelengths, with no other wavelengths produced.

d. The wires and clips yield zero resistance.

e. other responses can be acceptable if they can be defended reasonably.

11. What are some sources of experimental error and how could these errors be minimized?

The assumptions in #10 are not realistic and therefore represent sources of error.

12. What is the percentage error in your calculated value for Planck’s Constant?

Values will be based on data collected by students.

Practice Problems

1. A. Calculate the energy of the photons that are absorbed and emitted by green fluorescent protein, based on the diagram above.

Absorbed:

f1 = c /1 , so f1 = 3 x 108/3.95 x 10-7 = 7.59 x 1014 Hz

E1 = hf1, so 6.63 x 10-34 x 5.89 x 1014 = 5.04 x 10-19 J, or 3.14 eV

f2 = c /2 , so f2 = 3 x 108 / 4.70x 10-7 = 6.38 x 1014 Hz

E2 = (0.4)hf2, so 0.4 x (6.63 x 10-34) x (6.38 x 1014) = 1.69 x 10-19 J, or 1.06 eV

Ea = E1 + E2, so E = 5.04 x 10-19= 1.69 x 10-19 = 6.73 x 10-19 J, or 4.2 eV

Emitted:

f3 = c /3 , so f3 = 3 x 108/5.09 x 10-7 = 5.89 x 1014 Hz

Ee = hf3, so Ee = 6.63 x 10-34 x 5.8 X 1014 = 3.91 x 10-19J, or 2.44 eV

B. Which frequency in question 1 has the most energy?

Blue has more energy because the frequency is greater for shorter wavelengths, and higher frequency waves have higher energy.

C. Using your knowledge of the electromagnetic spectrum, is this electromagnetic radiation visible to humans? Explain.

Yes, humans can see wavelengths between 380 and 750 nm.

2. An ultraviolet light source has irradiance of 2 Watts/cm2. If this light shines on 1 square centimeter of bacterial cells on a Petri plate for 10 minutes, how many Joules of energy is this. If the light has a wavelength of 365 nm, how many photons of UV is this?

2 Watts x 1 cm2 = 1 watts = 2 Joules/second

2 Joules/second x 600 seconds = 1200 joules

3 x 108 m/s / 365 x 10-9 m = 8.2 x 1014 cycles/sec

8.2 x 1014 cycles/sec x 6.62 x 10-34Js = 5.4 x 10-19Joules for every photon of this light

1200 joules / 5.4 x 10-19Joules/photon =2.2 x 1021 photons. (Compare this to a mole, 6.02 x 1023).