Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Make sure there is a smooth, hard floor space (such as tile, concrete, wood or stone) for students completing the Quantum Leap activity so the marbles will bounce. Carpeted floors or rough surfaces will not work.
2. Lay out all 6 decks of Radioactive Decay Cards, one for each student at the activity station.

Safety Precautions

Power supplies and spectrum tubes operate at very high voltages and can produce a large electric shock. Do not touch the ends of the tube when the power supply is on. Do not touch the contacts on the transformer when the power is on. Always turn off the power supply before inserting, removing or adjusting the position of the spectrum tube. Spectrum tubes typically emit ultraviolet radiation, which is damaging to the eyes. Wear safety glasses or goggles that offer UV protection by filtering UV radiation. Spectrum tubes may get very hot. Never touch a spectrum tube when the power is on. After turning off the power, allow the tube to cool before removing it from the power supply. Please follow all laboratory safety guidelines. Do not handle broken glass with your hands, but use a dustpan and brush to clean up the pieces, and dispose of them properly in the appropriate receptacle.

Disposal

The carbon paper target sheets may be disposed of in a proper waste receptacle. All other materials may be stored for future use.

Lab Hints

• These laboratory activities can be completed in two 50-minute class periods. Preactivity Questions may be completed before lab begins the first day. 
• Explain to students that rolling 20 dice 5 times is equivalent to rolling a set of 100 dice just once. After the first set of 100 dice has been rolled, students must calculate how many times they must roll their dice in the next round and in each subsequent round.
• Alternatively, cups may be used to shake the dice and then quickly inverted to roll the dice.
• Encourage students to practice dropping a marble and having their partner catch it after the very first bounce. If marbles are allowed to bounce a second time, the second bounce marks will be fainter and will not represent the same amount of kinetic energy as the first drops. Make sure that students drop the marbles rather than throw them. The throws usually leave skid marks in the target sheet. For best results, each marble should be dropped from the same height and the same position every time. Sometimes a student may take the easy way out and simply stamp the paper with the marble held in his/her hands. Watch for an overly regular hit pattern.
• Using a spectroscope is an interesting and fun activity. Instructors may be discouraged from doing an “atomic spectra” lab because of the expense involved in purchasing power supplies. Many inexpensive alternatives to spectrum tubes are readily available. “Neon” novelty lamps (available at many party stores and discount stores) are good sources of bright line emission spectra of mercury (blue) and neon (red).
• The “Spectrum Analysis Chart” available from Flinn Scientific (Catalog No. AP8676) is a poster-size, full-color chart that shows the bright line emission spectra of ten elements.

Teacher Tips

• Take advantage of Internet resources to locate full-color reference spectra for different gases. The following websites (accessed October 2015) show a wide selection of atomic spectra:

  http://astro.u-strasbg.fr/~koppen/discharge
  http://hyperphysics-phys-astr.gsu.edu/hbase/hframe.html (see Quantum Physics section).

• Consider having students drop the marble from an even greater height (such as standing on a chair) to illustrate a 3s orbital and to compare the location of the marks made by the marble in the six areas on the target sheet.
• The Quantum Leap activity is not meant to be a model for p, d or f orbitals; it is meant to illustrate s orbitals.
• Prior to performing this lab, students should have had exposure to the concept of a photon and electromagnetic wave spectrum. Students should also be familiar with core optics ideas such as refraction and diffraction.
• Students may need guidance when attempting to reason what an absorption spectrum looks like from the information at hand. Probe students with guiding questions to aid them in their reasoning. Questions about the specific energy required to transition to higher energy states as compared to the specific energy required to transition to lower energy states may be beneficial.

Further Extensions

Opportunities for Inquiry
Challenge students to come up with an experimental model to simulate the build-up and decay of daughter isotopes in a radioactive decay series.

Alignment to the Curriculum Framework for AP^® Physics 2 

Enduring Understandings and Essential Knowledge
The internal structure of a system determines many properties of the system. (1A)
1A4: Atoms have internal structures that determine their properties. a. The number of protons in the nucleus determines the number of electrons in a neutral atom. b. The number and arrangements of electrons cause elements to have different properties. c. The Bohr model based in classical foundations was the historical representation of the atom that led to the description of the hydrogen atom in terms of discrete energy states (represented in energy diagrams by discrete energy levels). d. Discrete energy state transitions lead to spectra.

The energy of a system is conserved. (5B)
5B8: Energy transfer occurs when photons are absorbed or emitted, for example, by atoms or nuclei. a. Transition between two energy states of an atom correspond to the absorption or emission of a photon of a given frequency (and hence, a given wavelength). b. An emission spectrum can be used to determine the elements in a source of light.

The electric charge of a system is conserved. (5C)
5C1: Electric charge is conserved in nuclear and elementary particle reactions, even when elementary particles are produced or destroyed. Examples should include equations representing nuclear decay.

Nucleon number is conserved. (5G)
5G1: The possible nuclear reactions are constrained by the law of conservation of nucleon energy.

At the quantum scale, matter is described by a wave function, which leads to a probabilistic description of the microscopic world. (7C)
7C1: The probabilistic description of matter is modeled by a wave function, which can be assigned to an object and used to describe its motion and interactions. The absolute value of the wave function is related to the probability of finding a particle in some spatial region. (Qualitative treatment only, using graphical analysis.)
7C2: The allowed states for an electron in an atom can be calculated from the wave model of an electron.

1. The allowed electron energy states of an atom are modeled as standing waves. Transitions between these levels, due to emission or absorption of photons, are observable as discrete spectral lines.

7C3: The spontaneous radioactive decay of an individual nucleus is described by probability.

1. In radioactive decay processes, we cannot predict when any one nucleus will undergo a change; we can only predict what happens on the average to large number of identical nuclei.
2. In radioactive decay, mass and energy are interrelated, and energy is released in nuclear processes as kinetic energy of the products or as electromagnetic energy.
3. The time for half of a given number of radioactive nuclei to decay is called the half-life.
4. Different unstable elements and isotopes have vastly different half-lives, ranging from small fractions of a second to billions of years.

7C4: Photon emissions and absorption processes are described by probability.

1. An atom in a given energy state may absorb a photon of the right energy and move to a higher energy state (stimulated absorption).
2. An atom in an excited energy state may jump spontaneously to a lower energy state with the emission of a photon (spontaneous emission).
3. Spontaneous transitions to higher energy states have a very low probability but can be stimulated to occur. Spontaneous transitions to lower energy states are highly probable.
4. When a photon of the right energy interacts with an atom in an excited energy state, it may stimulate the atom to make a transition to a lower energy state with the emission of a photon (stimulated emission). In this case, both photons have the same energy and are in phase and moving in the same direction.

Learning Objectives
1A4.1: The student is able to construct representations of the energy-level structure of an electron in an atom and to relate this to the properties and scales of the systems being investigated.
5B8.1: The student is able to describe emission or absorption spectra associated with electronic or nuclear transitions as transitions between allowed energy states of the atom in terms of the principle of energy conservation, including characterization of the frequency of radiation emitted or absorbed.
5C1.1: The student is able to analyze electric charge conservation for nuclear and elementary particle reactions and make predictions related to such reactions based upon conservation of charge.
7C1.1: The student is able to use a graphical wave function representation of a particle to predict qualitatively the probability of finding a particle in a specific spatial region.
7C3.1: The student is able to predict the number of radioactive nuclei remaining in a sample after a certain period of time, and also predict the missing species (alpha, beta, gamma) in a radioactive decay.
7C4.1: The student is able to construct or interpret representations of transitions between atomic energy states involving the emission and absorption of photons. [For questions addressing stimulated emission, students will not be expected to recall the details of the process, such as the fact that the emitted photons have the same frequency and phase as the incident photon; but given a representation of the process, students are expected to make inferences such as figuring out from energy conservation that since the atom loses energy in the process, the emitted photons taken together must carry more energy than the incident photon.]

Science Practices
1.1 The student can create representations and models of natural or man-made phenomena and systems in the domain.
1.2 The student can describe representations and models of natural or man-made phenomena and systems in the domain.
1.4 The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively.
6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models.
7.1 The student can connect phenomena and models across spatial and temporal scales.
7.2 The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understandings and/or big ideas.

Answers to Prelab Questions

Activity 1—Radioactivity and Half-Life

1. What is the probability that a coin will decay after one coin toss?

   The probability that a coin will decay after one coin toss is 50%.

2. Using the definition of half-life provided in the Background, what is the “half-life” of the coins?

   The half-life is the amount of time it takes for half of a radioactive decay sample to decompose. The “half-life” of the sample of coins is one coin toss.

Activity 2—Radioactivity Decay Cards

1. The radioisotope chlorine-36 breaks down by alpha decay. (a) Look up the atomic number of chlorine. How many protons and neutrons are present in chlorine-36? (b) How many protons and neutrons does the resulting daughter isotope contain? (c) Identify the element and the mass number of the daughter isotope.
   1. Chlorine-36 has 17 protons and 19 neutrons.
   2. The resulting daughter isotope has 15 protons and 17 neutrons.
   3. Phosphorus-32 is the daughter isotope.
2. The radioactive isotope carbon-14 turns to stable nitrogen-14 under what decay process? Hint: The “-14” indicates the atomic mass of the isotope.

   In order for carbon-14 to become nitrogen-14, there must be an increase of one in the proton number, but the mass number must remain the same. This indicates that a neutron decayed into a proton and electron, which occurs during beta decay.

Activity 3—Atomic Structure and the Hydrogen Spectrum

1. What aspect of Bohr’s original model of electron structure is still present in the currently accepted theory of electron structure?

   The current theory of the electron structure of atoms retains the idea of quantized energy levels originally proposed by Niels Bohr to account for the line spectrum of hydrogen.

2. Assume that a certain atom has a total of four possible energy levels and that an electron can “jump” up or down between any of these energy levels. Draw a model of these energy levels similar to Figure 1 in the Background and use it to predict how many different spectral lines should be observed in the emission spectrum of the element.
   {14020_PreLabAnswers_Figure_7}
   Six electron transitions are possible among these four energy levels. Six spectral lines should be observed in the emission spectrum.

Activity 4—A Quantum Leap

1. What aspect of Bohr’s original model of electron structure is no longer considered valid in the currently accepted theory of electron structure?

   The current theory of the electron structure of atoms rejects the idea that the path of the electron is restricted to certain specific orbits around the nucleus. Modern theory states that it is impossible to describe the specific location of an electron as a particle at any given time.

2. Read through the procedure for the activity below. What components of the Target Sheet are analogous to atomic structure components such as the nucleus, electron, atomic orbitals and energy states?

   The bull’s eye, marble, and areas 1–6 are analogous to the nucleus, electron and atomic orbitals, respectively. The dropping of the marble from waist-level and eye-level can be viewed as representations of electrons transitioning down from different energy states. The density of the marks left by the marble represent the probability of finding an electron in a region of space.

Sample Data

Activity 1—Radioactivity and Half-Life

Number of sides on the dice: 6
“Decay” number: 3

Analyze the Results

• Graph the results obtained for the “radioactive decay” of dice. One axis should represent the number of dice remaining (nuclei) while the other must represent the number of rounds (time passed). (In this example, six-sided dice were used.)
  {14020_Data_Figure_8}
• Determine the half-life. Explain the method used to determine this value.

  Choosing two points in the y-axis where the first point is about twice as large as the second point, we compare the results for round 3 (65 dice) and round 6 (34 dice). Three rounds are required for approximately one-half of the dice to decay. The estimated half-life is three rounds.

• Is the half-life a “constant” number for the decay of the dice? How can you verify your answer?

  We can verify half-life simply by choosing another set of two points in the y-axis and comparing to our previous answer. Compare the results of round 5 (45 dice) and round 8 (22 dice)—three rounds are required for approximately one-half of the dice to decay. The half-life appears to have a constant value (t_½ = 3 rounds). However, as the number of dice being rolled decreases, the half-life is no longer constant. Radioactive decay is a random process. Large numbers of dice are needed to simulate a random process.

• Compare the value of the half-life and shape of your graph with that obtained by your partner using the alternate set of dice. Explain, based on probability, the difference in half-life values.

  The values for half-life are different for the four-sided and the six-sided dice. The four-sided dice have a higher probability of decay (¼ or 25%) than the six-sided dice (1/6 or 16.7%). Therefore, the decay curve for the four-sided dice goes to zero in a shorter amount of time. The shape of the two curves, however, are similar in that they both correlate to an exponential decay curve.

• Compare the value of the half-life with that obtained by another group using the same-sided dice but a different “decay number.” Does the half-life depend on the “decay number” that was chosen? Explain, based on probability.

  The half-life for six-sided dice does not depend on the “decay number” that was selected. There is an equal probability (1/6 or 16.7%) of rolling a decay number.

• Using the concept of half-life, predict the number of rounds that would be needed to reduce the number of dice from 10,000 to 625 using 6-sided dice and one “decay” number.

  Each arrow in the following sequence represents one half-life (3 rounds). Four half-lives (12 rounds) would be needed to reduce the number of dice from 10,000 to 625.
  10,000 → 5000 → 2500 → 1250 → 625

Activity 2—Radioactivity Decay Cards

Analyze the Results

• After putting the cards in order, make a graph of mass number (y-axis) vs. atomic axis (x-axis) for each element in the series. Write the element’s symbol at its point on the graph and connect the appropriate points in order of decay with an arrow.
  {14020_Data_Figure_9}
• Give one example each for an alpha decay equation and a beta decay equation from the graph.

  {14020_Data_Reaction_1}

• Explain qualitatively how beta and alpha decay adhere to the principle of conservation of charge.

  Alpha and beta decay adhere to the principle of conservation of charge because in any nuclear reaction the net value of electric charge does not change. For example, when a neutron (a neutral particle) undergoes beta decay, a net neutral charge is conserved by the formation of a proton and electron, which are electrically equal and opposite.

Activity 3—Atomic Structure and the Hydrogen Spectrum
Analyze the Results

• What is unique about a spectrum obtained for a florescent light? What element is used in fluorescent light fixtures?

  The fluorescent light exhibited a bright line spectrum superimposed on the continuous visible spectrum. The bright line spectrum corresponded closely to that of mercury, suggesting that mercury gas is used in fluorescent light fixtures.

• Discuss any interesting features of other types of light sources that were examined. Is it possible to identify the gases used in other light sources based on their emission spectra?

  Answers will vary. It was interesting to discover that a blue-colored novelty lamp advertised as “neon” lamp did not contain neon. The bright line spectrum of the blue “neon” lamp matched that of mercury. (Many blue “neon” lights also contain argon.) Only red neon signs actually contain neon! Other gases, such as mercury and argon are used to create other colors of neon lights. Many communities have switched low-pressure sodium lamps for streetlights. The streetlight that was examined had many lines in common with the atomic spectrum of sodium. The streetlight gave a bright spectrum as opposed to a continuous spectrum.

• When a continuous spectrum propagates through a cooler gas and is observed through a spectroscope, an absorption spectrum is observed. Based on your understanding of emission spectra and electron energy states and the information provided in the Background, what would an absorption spectra look like for hydrogen gas?
  {14020_Data_Figure_10}
  If excited gas atoms transmit specific photons when returning to lower energy states, then it can be concluded that a nonexcited gas absorbs specific energy photons to jump up to higher energy states. This would be portrayed as dark bands on top of the continuous spectrum provided by the light source behind the cooler gas. The positions of these dark bands on the spectrum correspond exactly with the positions of the emission spectral lines for specific elements.
• Is it possible to identify gases near sources of white light based on their absorption spectrum? Explain qualitatively how this method may be used to determine the chemical composition of the atmosphere of distant stars.

  Yes, this is possible by the same reasoning that it is possible to identify elements in a compound by their emission spectra. Stars, like the Sun, create a continuous spectrum due to the extreme energy emitted by the core. This energy escapes the core and propagates through the solar atmosphere that contains relatively cooler elemental gasses. The gases absorb specific wavelengths of energy. When viewed with a spectroscope, dark lines are observed on the spectrum of the Sun that correspond to the absorption spectra of hydrogen, helium and other gases contained in the solar atmosphere. Analyzing the absorption spectra of distant stars can, in turn, be used to deduce their chemical compositions.

• According to Equation 1 in the Background, the energy of light is inversely proportional to its wavelength—as the wavelength increases, its energy decreases. Based on the spectrum observed for incandescent white light, rank the colors of the visible spectrum from highest energy to lowest energy.

  Highest energy to lowest energy: Violet > blue > green > yellow > orange > red.

Activity 4—A Quantum Leap Analyze the Results

• Create a data table for your collected data that represents the hits in areas 1–6.
  {14020_Data_Table_3}
• Construct a bar graph for each target sheet. Label the horizontal axis as “area number,” and the vertical axis as “number of hits.”
  {14020_Data_Figure_12}
• How do the shapes of the bar graphs compare to the shape of the wave function shown in Figure 2?

  The graphs are similar in shape in that if one traces a curve over the bar graphs, both the bar graphs and Figure 2 look like a “bell curve.” The higher the height of the curve, the higher the probability of a marble mark (electron location) at the specific area (orbital) on the target sheet.

• Is there any way to predict the exact location of any one marble drop on the target? Explain.

  No, there is not a way to predict the specific (or exact) place that the marble would land on the target, since both sheets received hits very close to the center and farther away from it. There is, however, a way to predict where the marble would probably hit, since the target sheet demonstrates the probability that any one marble would land in a certain place (i.e., area 2). Note that the more data points (drops) there are, the more accurate the prediction will be as to where any certain marble would probably land.

• Describe the relationship between the energy of an electron, and its probable distance away from the nucleus of an atom.

  As the energy of the electron increases, the probability of being further from the nucleus increases.

Answers to Questions

1. The graph below represents a two-step decay series model for a radioisotope. Correctly key the three curves as either parent isotopes (4-sided dice), radioactive “daughter” isotopes (six-sided dice), or non-radioactive products of decay (buttons). Explain your reasoning.
   {14020_Answers_Figure_13}
   The “diamond” marked series must be the parent isotope (four-sided dice) because at “round zero” it is the only series with a non-zero value. It also has a faster rate of decay compared to the six-sided daughter isotope that is portrayed in the comparatively steeper slope of the diamond curve. The “square” marked series must be the daughter isotope because as the parent isotope decays, the daughter isotope number begins to rise. After a few rounds, the daughter isotopes (six-sided dice) begin to decay at a slower rate than the parent isotopes (four-sided dice) due to the lower probability of “decay.” The triangle series must be the non-radioactive products of decay because it is the only curve that does not match the shape of an exponential decay curve. As the radioactive elements decay, the number of buttons rises exponentially and then stabilizes as nearly all radioactive isotopes have decayed.
2. Identify the chemical composition of the atmosphere of the Sun and two unknown stars by analyzing their respective absorption spectra.
   {14020_Answers_Figure_14}
   The solar atmosphere contains hydrogen and helium. Unknown 1 is composed of hydrogen, sodium and calcium. Unknown 2 is composed of calcium and helium.
3. Identify the missing species (alpha particle, beta particle or nuclide) in the Thorium-232 decay series.
   {14020_Answers_Figure_15}
4. Following is a representation of the wave function for a particle.
   {14020_Answers_Figure_16}
   1. What does the area under the curve represent?

      The area under the curve represents the probability of finding a particle at a specific position in space.

   2. Rank, in order of highest to lowest, the regions A–F by the probability of finding the particle in the respective region.

      In order of highest to lowest: A > B > E > C > D.

References

AP^® Physics 1: Algebra-Based and Physics 2: Algebra-Based Curriculum Framework; The College Board: New York, NY, 2014.

Introduction

At the turn of the 19th century, a significant portion of the physics community believed that “almost everything is already discovered, and all that remains is to fill in a few holes.” The work of bold innovative minds tackling the mysteries of blackbody radiation and radioactive decay led to the development of quantum mechanics. Probabilistic and approximation methods thrive where classical solutions fail to account for atomic-scale phenomena.

Concepts

• Probability
• Absorption and emissions spectra
• Electron energy states
• Conservation of energy
• Radioactive decay
• Quantization of energy

Background

Since the time of ancient Greece, philosophers have yearned to uncover what everything is made of. The word “atom,” coined by the Greeks, means indivisible and was the historical birth of atomic theory: Everything is made of tiny indivisible particles. Throughout the years, significant progress has been made in our knowledge of the atom. John Dalton provided the first evidence-based atomic theory in the 1800s and concluded that an atom is the smallest unit of matter that still retains the properties of a chemical element.

The study of the elements and coinciding improvements in the manufacturing of glass used in prisms, led to the interesting observation that each chemical element is associated with a unique spectrum. When white light strikes a prism (or the grooves on a diffraction grating), the light is separated, or diffracted, into its component wavelengths known as a spectrum (plural—spectra). Scientists observed that when ionic compounds (i.e., sodium chloride, copper(II) sulfate) were added to alcohol flames, the light emitted produced a distinct pattern of bright, colored lines instead of the familiar “rainbow” spectrum. The series of bright lines is called an atomic emission spectrum and is unique to each element.

The cause of emission spectra remained a mystery until the structure of the atom and, in particular, its electronic structure, was solved. The subsequent discoveries of the electron and nucleus in the late 19th century led to a model of the atom, proposed by Niels Bohr, that would explain the phenomena of atomic spectra. Bohr’s model proposed that an electron is restricted to specific orbits around the nucleus of the atom. These orbits differ in their distance from the nucleus and their energy levels. Electrons that are closer to the nucleus are lower in energy than electrons that are farther away from the nucleus. This idea is called the quantization of energy—electrons can only occupy specific energy levels. Electrons may not have intermediate energy levels between these allowed states.

For an electron to be “excited” or promoted from a lower energy level to a higher energy level, it must absorb energy of a specific wavelength. Conversely, an electron may randomly release energy to transition from a higher energy level to a lower energy level. This release in energy can be understood with the principle of conservation of energy. When the potential energy is reduced from a higher energy level to a lower energy level, the change in potential energy must turn into some other form of energy. This energy is manifested as a photon of a specific wavelength emitted by the electron.

Bohr’s theory successfully predicted the atomic spectrum emitted by excited hydrogen gas. When electrical energy is supplied to hydrogen atoms in a spectrum tube, the atoms absorb energy and the electrons are promoted to excited energy levels. Once excited, however, the electrons have a natural tendency to drop back down to a lower energy level by emitting light of the appropriate wavelength and energy. The emitted light for a given transition is observed through a diffraction grating as a bright line in the emission spectrum of hydrogen.

The relationship between the energy of light and its wavelength is given by Planck’s law:

ΔE is the difference in energy between the two energy levels in joules, h is Planck’s constant (h = 6.626 x 10^–34 J•sec), c is the speed of light, and λ is the wavelength of light in meters.

The emission spectrum for hydrogen exhibits four bright lines in the visible region of the electromagnetic spectrum (see Figure 1). The Bohr model was found to be very successful for the structure of the hydrogen atom, but it failed to hold true for atoms of two or more electrons. The development of quantum mechanics in the 1920s built on the idea of quantized energy levels and introduced the idea of the wave nature of matter to describe the properties of electrons. Quantum mechanics describes the motion of small particles confined to microscopic regions of space. According to quantum mechanics, the location of an electron is not restricted to specific orbits but can only be defined in terms of the probability of finding an electron. This probabilistic description can be modeled by a wave function, and when this function is assigned to an object (like and electron) it can be used to describe its motion and interactions. The absolute value of the electron wave function is directly related to the probability of finding an electron in some region of space (see Figure 2). Therefore, the exact positon of an electron at any given instant is not specified; nor is the exact path that the electron takes about the nucleus. Physically, the orbit model of electron energy levels is abandoned and replaced with a system of atomic orbitals. An atomic orbital is the most probable region in space where an electron of specific energy may be found at any given time around the nucleus. Atomic orbitals differ in their size, shape, and orientation in space, and also in their energy. The characteristic atomic emission spectrum of an element can be interpreted based on the unique arrangement of atomic orbital energy levels for its atoms.

Progress in atomic theory and improvements in the understanding of nuclear structure, such as the discoveries of the neutron and proton, shed light on the mysterious process behind the phenomenon of radioactive decay first observed by Henri Bequerel in 1896. Some isotopes of certain elements, or nuclides, are radioactive—their nuclei spontaneously break apart because the nuclear force holding the protons and neutrons together is not strong enough. A nuclide is a unique atom, represented by the symbol where X is the symbol for the element, A is the mass number or total number of neutrons and protons, and Z is the atomic number or total number of protons in the nucleus.

The breaking up of a nucleus is known as radioactive decay and is a spontaneous and completely random process. One way radioactive decay occurs is by alpha decay. When alpha decay occurs, alpha particles identical to a helium nucleus (two protons and two neutrons) are emitted from the nucleus. This produces an atom of a different element and a mass number that is four atomic mass units less (see Figure 3). Beta decay occurs when a neutron decays into a proton and an electron, and the electron (called a beta particle) is emitted at a high rate of speed from the nucleus. The mas number of the atom does not change, but since the nucleus now has one more proton than before, the atomic number increases by one and a different element results (see Figure 4). Like other microscopic processes, the rate of radioactive decay can only be described by probability; physicists cannot accurately predict the exact point when a single atom will undergo decay. Different nuclei decay at different rates via different processes. These different rates of decay vary widely from seconds to billions of years. A convenient way to describe the rates of decay of different nuclides is to compare their half-lives. A half-life (t_½) is described as the time required for one half of the nuclides to undergo radioactive decay. The half-life is a constant for each radioactive nuclide. Equation 2 is used to calculate the amount of nuclides remaining after a certain amount of time has passed. N is the number of nuclides remaining after time t has passed, N₀ is the initial number of nuclides at time t = 0, k is the radioactive decay constant, and t is the amount of time passed.

Experiment Overview

This advanced inquiry lab uses a guided-inquiry activity station approach with four self-contained labs that can be completed in any order:

• Investigate the probabilistic nature of radioactive decay through a half-life simulation using dice.
• Radioactive decay cards are used to analyze the beta and alpha particle emissions in radioactive decay.
• Examine the hydrogen spectrum and extrapolate its absorption and emission spectra to deduce unknown chemical compositions of different spectra.
• Creatively determine the uncertainty principle and its relation to the location of electrons in their orbitals.

Materials

Prelab Questions

Activity 1—Radioactivity and Half-Life
The random process of a coin toss is a simple model of radioactive decay. The following expriment was conducted: 100 coins were placed heads-up in a box. The box was shaken and all coins that landed tails or “decayed” were removed from the box. This was repeated a total of eight times. Study the graph below and answer the following questions.

1. What is the probability that a coin will decay after one coin toss?
2. Using the definition of half-life provided in the Background, what is the “half-life” of the coins?

Activity 2—Radioactivity Decay Cards

1. The radioisotope chlorine-36 breaks down by alpha decay. (a) Look up the atomic number of chlorine. How many protons and neutrons are present in chlorine-36? (b) How many protons and neutrons does the resulting daughter isotope contain? (c) Identify the element and the mass number of the daughter isotope.
2. The radioactive isotope carbon-14 turns to stable nitrogen-14 under what decay process? Hint: The “-14” indicates the atomic mass of the isotope.

Activity 3—Atomic Structure and the Hydrogen Spectrum

1. What aspect of Bohr’s original model of electron structure is still present in the currently accepted theory of electron structure?
2. Assume that a certain atom has a total of four possible energy levels and that an electron can “jump” up or down between any of these energy levels. Draw a model of these energy levels similar to Figure 1 in the Background and use it to predict how many different spectral lines should be observed in the emission spectrum of the element.

Activity 4—A Quantum Leap

1. What aspect of Bohr’s original model of electron structure is no longer considered valid in the currently accepted theory of electron structure?
2. Read through the procedure for the activity below. What components of the Target Sheet are analogous to atomic structure components such as the nucleus, electron, atomic orbitals, and energy states?

Safety Precautions

Power supplies and spectrum tubes operate at very high voltages and can produce a large electric shock. Do not touch the ends of the tube when the power supply is on. Do not touch the contacts on the transformer when the power is on. Always turn off the power supply before inserting, removing or adjusting the position of the spectrum tube. Spectrum tubes typically emit ultraviolet radiation, which is damaging to the eyes. Wear safety glasses or goggles that offer UV protection by filtering UV radiation. Spectrum tubes may get very hot. Never touch a spectrum tube when the power is on. After turning off the power, allow the tube to cool before removing it from the power supply. If the unlikely case of a cracked marble, do not handle the glass with your hands, but use a dustpan and brush to clean up the pieces and dispose of them properly in the receptacle indicated by the instructor. Please follow all laboratory safety guidelines.

Procedure

Activity 1—Radioactivity and Half-Life

1. With a partner, obtain a set of 4-sided and 6-sided dice.
2. Pick one decay number for your set of dice. Note: Pick a number between 1 and 4 if using the 4 sided dice or between 1 and 6 if using the 6 sided dice; your partner will have the alternate set.
3. Create a data table to keep track of the number of nuclei remaining after multiple rounds of decay as well as being able to record all relevant variables. Hint: Consider the coin toss example from the Preactivity Questions.
4. Roll all 20 dice in a box or on a table top. Re-roll any dice that do not land flat.
5. Assume that any dice landing on the decay number have “decayed.” Record the number of dice that decayed in a data table.
6. Repeat steps 2 and 3 until the dice have been rolled 5 times (for a combined total of 100 dice rolls.) After each roll, record the number of dice with the assigned decay number.
7. Add together the number of dice that decayed and record this number.
8. Subtract the number of dice that decayed from the initial number of dice (100) to determine the number of dice remaining. Record the number of dice remaining; this will be the initial number of dice for a second round.
9. Repeat steps 4–8. Roll the dice as many times as needed to match the number of initial dice for round two. Record all data. For example, if 79 dice remain after the first round, then the 20 dice would be rolled three times, and then 19 dice would be rolled once so that the total number of dice rolled in the second round is equal to 79 [(20 x 3) + 19 = 79].
10. Repeat step 9 until no dice remain or until 20 rounds of “radioactive decay” have been completed.

Analyze the Results

• Graph the results obtained for the “radioactive decay” of dice. One axis should represent the number of dice remaining (nuclei) while the other must represent the number of rounds (time passed).
• Determine the half-life. Explain the method used to determine this value.
• Is the half-life a “constant” number for the decay of the dice? How can you verify your answer?
• Compare the value of the half-life and shape of your graph with that obtained by your partner using the alternate set of dice. Explain, based on probability, the difference in half-life values.
• Compare the value of the half-life with that obtained by another group using the same-sided dice but a different “decay number.” Does the half-life depend on the “decay number” that was chosen? Explain, based on probability.
• Using the concept of half-life, predict the number of rounds that would be needed to reduce the number of dice from 10,000 to 625 using 6-sided dice and one “decay” number. Repeat the calculation using 10-sided dice and two “decay” numbers.

Activity 2—Radioactivity Decay Cards
In this activity, the order of natural decay of a radioactive element (U-238) to a stable species (Pb-206) must be determined. There will be thirteen (13) nuclide species between U-238 and Pb-206, and each radioactive decay will emit an alpha or beta particle. Arrange the element cards in order of the natural radioactive decay with either an alpha or beta particle between each element.

Analyze the Results

• After putting the cards in order, make a graph of mass number (y-axis) vs. atomic axis (x-axis) for each element in the series. Write the element’s symbol at its point on the graph and connect the appropriate points in order of decay with an arrow.
• Give one example each for an alpha decay equation and a beta decay equation from the graph.
• Explain qualitatively how beta and alpha decay adhere to the principle of conservation of charge.

Activity 3—Atomic Structure and the Hydrogen Spectrum

1. Using the handheld spectroscope, observe the continuous “rainbow” spectrum from an incandescent lightbulb.
2. Observe the colors of light on the visible spectrum and the wavelength range for each color band. Sketch the spectrum of white light using colored pencils.
3. (Optional) For optimum viewing of the emission spectra of gas discharge tubes using a handheld spectroscope, stabilize the spectroscope on a support stand. Set up a support stand in front of the power supply and attach one ring clamp. Place the spectroscope on the ring clamp and adjust the height of the ring clamp so that the eyepiece on the spectroscope is approximately level with the middle of the gas discharge tube. Attach a second ring clamp on top of the spectroscope so that it will be held firmly in positon without moving.
4. With the power OFF, insert the hydrogen spectrum tube between the contacts on the power supply.
5. Move the spectroscope so that it is about 3–5 cm away from the spectrum tube.
6. Turn on the power supply, and observe the atomic emission spectrum of hydrogen. Work with a partner to note the principal features in the hydrogen spectrum.
7. Turn OFF the power supply. Record the following information in a data table for the emission spectrum of hydrogen: the number of lines, their colors, and their approximate wavelengths.
8. Using colored pencils, sketch the atomic spectrum of hydrogen. Turn the power supply on and off, as necessary, to complete the observations in step 7.
9. Using the handheld spectroscope, observe the spectrum of visible light obtained from a fluorescent light. What kind of spectrum is produced? If any bright lines are present, record the number of lines, their colors, and their approximate wavelengths.
10. (Optional) Using a handheld spectroscope, observe the emission spectrum of other light sources, such as neon signs, streetlights, headlights, novelty lamps, etc. What kind of spectrum is produced? If any bright lines are present, record the number of lines, their colors, and their approximate wavelengths.

Analyze the Results

• What is unique about a spectrum obtained for a florescent light? What element is used in fluorescent light fixtures?
• Discuss any interesting features of other types of light sources that were examined. Is it possible to identify the gases used in other light sources based on their emission spectra?
• When a continuous spectrum propagates through a cooler gas and is observed through a spectroscope, an absorption spectrum is observed. Based on your understanding of emission spectra and electron energy states and the information provided in the Background, what would an absorption spectra look like for hydrogen gas?
• Is it possible to identify gases near sources of white light based on their absorption spectrum? Explain qualitatively how this method may be used to determine the chemical composition of the atmosphere of distant stars.
• According to Equation 1 in the Background section, the energy of light is inversely proportional to its wavelength—as the wavelength increases, its energy decreases. Based on the spectrum observed for incandescent white light, rank the colors of the visible spectrum from highest energy to lowest energy.

Activity 4—A Quantum Leap

1. Obtain one waist-level target sheet set for your group. Note: Carbonless paper is a special “non-carbon” paper consisting of two attached sheets—one white, one yellow—that make an imprint on the bottom sheet when an object strikes the top sheet.
2. Choose one person to be the “Target Aimer” and one person to be the “Marble Catcher.” Lay the waist-level target sheet on a smooth, hard floor.
3. The “Target Aimer” should hold a glass marble in one hand over the center of the target. Bend the elbow at the waist so that the forearm is parallel to the floor and perpendicular to the body.
4. Have the “Marble Catcher” kneel down next to the target sheet and be prepared to catch the marble after the first bounce. Note: Practice bouncing the marble on the floor first to be sure the “Catcher” catches it.
5. The “Target Aimer” should carefully drop (do not throw!) the marble from waist level, aiming for the bull’s-eye. The “Marble Catcher” should catch the marble after the first bounce to be sure the marble doesn’t leave more than one mark per drop on the target sheet.
6. Repeat this dropping procedure approximately 100 times over the same target. The “Catcher” should make a tally mark after each drop on a separate sheet of paper for ease of counting. Each hit should leave a mark on the bottom yellow sheet.
7. After 100 drops, carefully separate the bottom yellow sheet from the top white sheet. Notice the pattern of the marks on the yellow sheet.
8. Obtain one eye-level target sheet set for your group and place your names at the top. This consists of two attached sheets—one white and one pink.
9. Repeat steps 2–6 above, with the “Target Aimer” and the “Marble Catcher” switching jobs. This time, use the eye-level target sheets. The “Target Aimer” should drop the marble with the arm fully extended from eye level, aiming for the bull’s eye. Try to drop the marble from the same eye-level height each time (100 drops).
10. When done, carefully separate the bottom pink sheet from the top white sheet. Again, notice the pattern of the marks on the pink sheet.

Analyze the Results

• Using a fine-lined pen or pencil, circle each mark made by the marble on both target sheets (yellow and pink.)
• Count the number of hits in each target area (1–5) by counting the number of circles. Be sure to also count the hits made outside areas 1–5 as area 6. For those spots that landed exactly on the line between two areas, count it as the lower number.
• Create a data table for your collected data that represents the hits in areas 1–6.
• Construct a bar graph for each target sheet. Label the horizontal axis as “area number,” and the vertical axis as “number of hits.”
• How do the shapes of the bar graphs compare to the shape of the wave function shown in Figure 2?
• Is there any way to predict the exact location of any one marble drop on the target? Explain.
• Describe the relationship between the energy of the electron, and its probable distance away from the nucleus of an atom.

Student Worksheet PDF

14020_Student1.pdf