LAB #8: Emission Spectra and the Electronic Structure of Atoms

LAB #8: Emission Spectra and the Electronic Structure of Atoms

Lab 8.1 Relating Wavelength, Frequency and Energy

Purpose - Lab 8.1

To relate wavelength, frequency and energy

Background:

The idea of atoms is as old as the ancient Greeks. The Greek philosopher, Democritus, coined the term atom for the smallest particle of matter. Based upon a particulate model of matter much like our model from IPS Democritus proposed the idea of atoms. Meanwhile, Aristotle proposed a continuous model of matter where there was no smallest piece. Until the 1800s atoms were merely an idea with no experimental evidence to support the existence of these tiny pieces of matter.

In the early 1800s John Dalton, an English school teacher, proposed the Atomic Theory based upon the experimental evidence of his contemporaries such as Lavioiser and Proust. Dalton proposed that all matter was composed of tiny indivisible atoms, much like a solid billiard ball. Lavoiser used the oxidation of metals to show conservation of mass and consequently atoms as well. The Law of Constant Composition was demonstrated in the work of Proust. (See your text for more details about Dalton’s Atomic Theory)

By the end of the 19th century, experimental evidence showed the existence of subatomic particles smaller than atoms. Thomson is credited with the discovery of electrons using the cathode ray tube. The mass to charge ratio of these particles suggested that they must be smaller than atoms and Dalton’s model of a solid indivisible model of the atom was modified. Thomson proposed the Plum Pudding Model of the atom with tiny electrons embedded in positive matrix. In the early 1900s the Gold Foil experiment of Ernest Rutherford showed that Thomson’s model would need revision to reflect a dense positively charged central nucleus surrounded by negative electrons. (See your test for more details about the Gold Foil experiment.)

Explaining the orbit of negatively charged electrons required that Rutherford ignore some of the laws of classic physics. In addition the emission spectrum of excited atoms could not be explained using Rutherford model of the atom. When atoms absorb energy they give off wavelengths of light but only of specific wavelengths. Niels Bohr attempted to explain this by modifying Rutherford’s model of the atom. Understanding the further developments of the atomic model require some understanding of the nature of light. Much like the initial debate over the nature of matter- particle or wave. The same debate still exists over the nature of light- particle or wave.

First we will investigate the wave model of light and then particle model of light.

The continuous spectrum of light observed through the spectroscope is a result of the diffraction and separation of light based on wavelength and frequency. White light from the sun and the glowing tungsten filament of a light bulb appear as a continuous spectrum because the light contains a range of wavelengths and frequencies.

The spectrum of electromagnetic radiation ranges from the short waves of gamma rays to the long waves of radio waves. The wavelengths visible to our eyes are between 4 x 10-7 m to 7.5 x 10-7 m. Since these numbers are quite small they are often reported in angstroms 10-12 m or nanometers (nm) 10-9 m. The frequency is related to wavelength. Frequency or the number of waves is limited by the constant speed of light and electromagnetic waves. The speed of light is 3.00 x 108 m/s.

Pre-Lab Questions:

1. Describe Dalton’s Atomic Theory. Include a list of the main points. Include the experimental evidence that he used to support his theory. Indicate an approximate year for Dalton’s work.

2. Describe Thomson’s model of the atom and the experimental evidence that lead him to propose this model. Indicate an approximate year for Thomson’s work.

3. Describe Rutherford’s model of the atom and the experimental evidence that lead him to propose this model. Indicate an approximate year for Rutherford’s work.

4. Why are atoms radioactive? Describe the three kinds of radiation.

Procedures:

A. Record observations of high, medium and low energy waves produced in the slinky demonstration. Compare the effect on both wavelength and frequency as the energy of the wave increases. Draw a labeled sketch to compare the waves.

B. Observe both sunlight and indoor fluorescent lighting through the spectroscope. Describe your observations.

Analysis:

5. How is the energy of the wave related the wavelength? Support with your observations of waves. Is the relationship direct or inverse? Write an equation showing these variables equal to a constant. Explain mathematically how this equation shows the relationship.

6. How is the energy of the wave related the frequency? Support with your observations of waves. Is the relationship direct or inverse? Write an equation showing these variables equal to a constant. Explain mathematically how this equation shows the relationship.

7. Describe the relationship between wavelength, frequency and the speed of light. Write an equation that relates the three. Explain how this equation reflects the relationship between wavelength and frequency.

8. Describe the relationship between frequency and the energy of the photon. Write an equation that relates the variables. When the frequency increases, what happens to the energy? Since Planck’s constant is a constant, explain how this equation reflects the relationship between frequency and energy.

9. a. Calculate the frequency of a radio wave with a wavelength of 4.3 x 103 m.

b. Calculate the energy of the radio wave with a wavelength of 4.3 x 103 m. Refer to the frequency calculated in # 5.

10. Calculate the frequency and energy of an x-ray with a wavelength of 2.1 x 10-10 m/wave.

11. Describe the electromagnetic spectrum. Compare and contrast gamma rays and radio waves. Compare the wavelength, frequency and energy.

12. Describe the visible spectrum of white light. Relate the colors of light to frequency, wavelength and energy.

LAB #8: Emission Spectra and the Electronic Structure of Atoms

Lab 8.2 Emission Spectrum of Selected Elements

BACKGROUND:

In 1913, Niels Bohr used the idea of a quantum of energy (discrete bundle or photon) introduced by Max Planck and the model of the nuclear atom introduced by Ernest Rutherford in 1911 to develop an explanation for the behavior of an electron around a hydrogen atom. He explained that the characteristic lines of the hydrogen atom spectrum were the result of electron movement from one energy level to another. The distinct energy levels could be calculated and were called quantum numbers.

Although Bohr's model could successfully explain the emission spectrum of hydrogen it could not be used to interpret the spectra lines atoms with more than one electron. The concept of different quantum levels remained, but additional calculations were necessary.

Our present theory of atomic structure states that electrons in atoms can possess only discrete energy values. The energy levels are characterized by an integer n called the principal quantum number. The electrons in atoms in their ground states exist in their lowest energy levels. If energy is supplied by an electrical discharge or heat, the atoms will absorb energy and electrons will enter higher energy levels. The energy levels may be compared to rungs on a ladder. The rungs are discrete rather than continuous; it is not possible to be in between rungs. Atoms having extra energy are called excited atoms. They can lose some of this extra energy in discrete amounts as the electrons drop back down. The energy is released as waves with distinct wavelengths, that correspond to the amount of energy released. The more energy released the shorter the wavelength. These discrete bundles of energy are called quanta or photons. A quantum of energy is the smallest level of energy that can be transferred to or from an atom or molecule. Photons possess energy proportional to the frequency. The proportionality constant is called Planck's constant. (E = hƒ)

The bright line spectra observed when atoms of gaseous elements are excited by an electric discharge show sharp lines of colored light with regions of no light. This provides convincing evidence that the electrons in atoms do not have a continuous range of energies but only certain discrete values of energy. It was discovered that each atom has distinct characteristic spectrum that could be used to identify that element.

Purpose: To use a simple spectroscope to observe the bright line spectra of different elements. To relate the bright line spectra to the energy of the electrons of excited atoms.

Pre-Lab Questions:

1. Describe the photoelectric effect. Explain why this cannot be explained by the wave model.

Procedures:

Observe and record the bright line spectra of the different elements

Label the ends of each spectrum. Which end is high energy? low energy?

Which band of colored light is the result of the fall from the highest level?

lowest level?

Which band of colored light is the lowest frequency? highest frequency?

Which colored band of light has the longest waves? shortest waves?

Analysis:

**2. Given the following data for hydrogen.

a. Calculate the frequency and energy of each observed line of light.

b. Tell the story of how this bright line spectrum was produced. Be detailed and specific about the movement of electrons between energy levels as energy is absorbed and released. Explain the different energy levels in terms of their distance from the nucleus and the potential energy and stability of an electron in those levels. Explain the lines produced in terms of the wavelengths, frequency and energy.

Also explain the lines undetected by the human eye in the range of infrared and ultraviolet.

HONORS: Use Bohr’s Equation.

Calculate the energy released as an electron in hydrogen falls from n = 3 to n = 2.

Which observed line in the spectrum is the result of this transition?

Calculate the energy released as an electron in hydrogen falls from n = 5 to n = 2.

Which observed line in the spectrum is the result of this transition?

Calculate the energy released as an electron in hydrogen falls from n = 3 to n = 1.

Explain why this line is not observed?

3. Given the following data for mercury.

Calculate the frequency and energy of each observed line of light.

Describe what happens to the atoms and their electrons within the tube when electric current passes through the tube. Explain how the observed bright line spectrum is produced. Discuss electron movement between energy levels when energy is absorbed and then when energy is released. You cannot be as detailed about mercury as you can about hydrogen, since you do not know the specific quantum number for the energy levels involved. You can only give a general description involving the relative enrgy levels without specific numbers.

4. Explain why the emission spectrum cannot be explained by the wave model.

5. What was the significant difference between Rydberg (1885) and Bohr’s (1911) equations?

6. Draw the electron configuration for each atom observed in the emission spectrum.