Lab Name: Spectroscopy Fingerprints in Light Author: Sean Lindsay, David McCallister, and Noah Frere Version 1.0 created [8/25/2018]  Learning Goals 

In this activity, the student will   ● use spectroscopy to identify elements ● learn about the electromagnetic spectrum of light ● understand light as a wave and as a particle ● learn what a spectrum is and what types of spectra are ● understand how spectra of elements serve as chemical “fingerprints” ● understand how light interacts with matter 

Materials 

● Vernier Spectroscopy Carousel Power Supply with Tubes ● Spectroscope ● Vernier LoggerPro3 Software  ● Vernier Emission Spectrometer 

 1. Background 

1.1 - Electromagnetic spectrum 

Nearly everything we know about the universe, we have discovered through looking at the                           light from celestial objects reaching Earth. Without the ability to investigate these objects                         directly, the light from them that reaches Earth offers our window into understanding                         everything from their brightness, size, composition, rotational properties, temperatures,                 densities, and magnetic field to the expansion of the universe itself. In order to extract this                               information from just the light, it is necessary that we understand the nature of light itself. It                                 is knowing the properties of light that allows us to learn as much as we do about our universe. 

When astronomers refer to light, they are not only referring to the light we observe in our                                 daily lives. They are also referring to types of light invisible to the human eye. The light                                 humans can see is referred to as visible (or optical) light. Some forms of life can see beyond                                   this range and see infrared light or ultraviolet light. You are probably familiar with both of                               these kinds of light. Infrared (IR) light, in quotidian human life, can be thought of as light from                                   heat. It is the energy that you feel as hot when you get near a hot object. Ultraviolet (UV) light                                       is why we wear sunscreen during the summer as it is the light that gives you a sunburn. There                                     are other kinds of light as well, and you have likely heard of most of them, but maybe not                                     realized they are light. The seven kinds of light are radio wave, microwave, infrared, visible,                             ultraviolet, X-ray, and gamma ray light. Taken together, we call this the electromagnetic                         spectrum (EM; Fig. 1). More formally, astronomers and physics know light as electromagnetic                         radiation. 

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The part of the electromagnetic spectrum humans can see is called the visual spectrum  

Why electromagnetic? Electromagnetic refers to the physical nature of light. We now                       understand that light really is a coupling between an oscillating electric field and magnetic                           field. It is a fundamental piece of a branch of physics knowns as electromagnetism because it                               deals with electric and magnetic parts, which are related and inseparable from one another. 

Why spectrum? Light can be divided up on a scale between two extremes, from radio waves                               to gamma rays. What aspect of light defines the scale? The division of the spectrum can be set                                   along the energy, wavelength , or frequency of the light. For energy, we need to understand                             light as particle. For wavelength and frequency, we must understand light as a wave. 

 Figure 1. The electromagnetic spectrum of light. 𝛄 is the Greek letter gamma. Image credit: Wiki-Creative                               Commons 

1.2 Light as a Wave 

 

 

Figure 2. The wavelength of light. Shorter wavelength is the same as higher frequency or higher                               energy. Wavelength of light is a physical distance. Visible light has wavelengths ranging from                           about 400 - 800 nm. 

Light can be considered as an oscillation in an electric field coupled to a perpendicularly                             oriented magnetic field. This oscillation is a type of wave called an electromagnetic wave.                           You are already likely familiar with several types of waves: waves on an ocean, sound waves,                               

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and perhaps even seismic waves. Waves are a host of general properties, and light, an                             electromagnetic wave , is no exception. Some important properties of waves are as follows: 

- Amplitude (A): size of the oscillation - Wavelength(λ): distance between successive identical parts of a wave (SI Unit: meter) - Frequency (ν): number of waves that pass through a point in one second(SI Unit:                           

Hertz or s-1) - Wave Speed(c): the rate of propagation of the wave. (SI Unit: m/s) 

Wavelength, or frequency, can be used to arrange the EM from short-to-long wavelength, or                           equivalently low-to-high frequency, where low frequency means small numbers and high                     frequency means large numbers. As seen in Figure 1, from short-to-long wavelength                       (low-to-high frequency) the parts of the EM spectrum are: Radio Waves, Microwaves, Infrared                         Light, Visible Light, Ultraviolet Light, X-rays, and Gamma Rays. You can think of each                           wavelength as a distinct “color” of light and they range from very large wavelengths (low                             frequencies)  

The wavelength is a measure of distance between the crests of the wave, and therefore is                               measured as a physical distance. The frequency is counting the number of wavelengths                         passing a point every second. For frequency, we use the unit Hertz (Hz). Hertz is a measure of                                   the number of cycles per second, and so in the case it is the number of wavelengths passing                                   every second.. When frequency is multiplied by the wavelength, you then have a total number                             of wavelengths, a total distance, passing every second. Note that this is how much distance in                               how much time, or rather a speed. Indeed, the speed of a wave is found by multiplying the                                   wavelength by the frequency. For light, the speed is always the same, c = 3.0 x 108 meters per                                     second (m/s), or roughly 186,000 miles per second. This speed is the same regardless of                             wavelength (or equivalently frequency), and is therefore simply referred to as the speed of                           light and indicated by a lower-case letter c. This provides the connection between the speed                             of light, the wavelength of light, and the frequency of light, which can be summarized by the                                 equation 

νc = λ  where c is the speed of light, λ is the wavelength, and 𝝂 is the frequency. 

A note on the speed of light: It is usually set by properties of the medium through which the                                     wave is moving. Electromagnetic waves in a vacuum move at a constant speed in all                             reference frames: c = 300,000,000 meters per second (186,000 miles per second). 

The part of the electromagnetic spectrum humans can see is called the visible spectrum , or                             sometimes the optical spectrum . From long to short wavelengths, it is divided in six colors:                             red, orange, yellow, green, blue, and violet (ROYGBV) with wavelengths centered near 680 nm                           for red, 610 nm for orange, 580 nm for yellow, 540 nm for green, 470 nm for blue, and 410 for                                         violet. The visible spectrum is shown in Fig. 1. 

1.3 Light as particle with energy. 

In a famous experiment in 1905, Albert Einstein was able to confirm German physicist Max                             Planck’s conjecture that light comes in distinct packets of energy referred to as “quanta”                           (singular: quantum). In this case, we say that light is quantized. The experiment                         

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demonstrated the photoelectric effect, but what it revealed about the nature of light was                           something much deeper. Light not only behaves as a wave, but it also behaves as a particle,                                 in strange wave-particle duality. As a particle, each packet of light, or quanta of light, carries                               a very specific energy that is related to the frequency of the light. This packet of energy is                                   what physicist’s refer to as a photon, and the amount of energy is called the photon energy. A                                   photon is a massless particle, but it does carry energy and momentum. The energy of a                               photon is proportional to its frequency meaning the higher (larger number) the frequency,                         more energy the photon has. Specifically, photon energy can be calculated by multiplying the                           frequency by Planck’s constant, h.  

 

ν E = h  

 

where h has a value of 4.137E-15 eV s. Using ν = c/λ, this formula can be re-written as 

 

E = λhc

 

 

Since, both h and c are constants, one can replace the quantity hc with the value of 1240 eV-                                       nm, if we use the units of eV for energy and nanometers (nm; 1 billionth of meter) for                                   wavelength. This gives the energy of a photon as function of wavelength: 

 

E = λ1240 eV nm  

 

Plugging in a wavelength measured in nanometers will yield a photon energy measured in                           electron volts (eV). An electron volt is the amount of energy that an electron has after being                                 accelerated through 1 volt of potential. While that might sound technical and obscure, you                           can think of it as an amount of energy that is convenient for measuring photon energies. 

Now the EM spectrum can be arranged from longest-to-shortest wavelength,                   lowest-to-highest frequency, or lowest-to-highest energy. We see that there is a way to                         translate from one value to another (wavelength to frequency, wavelength to energy,                       frequency to energy) if the correct equation is applied. More so, understanding light as a                             particle called a photon allows us to understand how light will interact with atoms and other                               kinds of matter. The interaction of light with matter is a branch of astronomy called                             spectroscopy. To understand this interaction, a model of the atom and how it responds to                             external sources of energy is needed. 

 

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1.4 Atomic Physics - Bohr Model 

While not our current quantum mechanical model and understanding of the atom, a very                           convenient model of the atom is called the Bohr model (Fig. 3). Building on the work of                                 others, in 1913, Niels Bohr and Ernest Rutherford advanced the model of the atom past that                               of a positively-charged nucleus containing protons and neutrons surrounded by negatively                     charged electrons. They realized, that like photons, the energies the electrons surrounding                       the could have came in discrete packets: the electron energies were quantized! In the Bohr                             model, the negatively-charged electrons orbit the positively-charged nucleus, but only a                     specific distances, or rather, the electrons are allowed to occupy only certain discrete energy                           levels. The distances and energies they are allowed to orbit at are called electron energy                             levels or electron orbitals.  The lowest energy an electron can have is called the ground state orbital, and it is labelled as                                   the n = 1 state. The next highest energy level is called the first excited state, or n = 2 state,                                          because the electron now has more energy, and is “excited.” The next highest is the second                               excited State (n = 3), and then the third excited state (n = 4), and so on and so forth. There is                                           limit to how much energy an electron can have and still be bound to the atom. This energy                                   limit is called the ionization energy . Give the electron more than the ionization energy, and                             the electron will no longer be bound to the atom, leaving a free electron and an atom that is                                     now missing an electron. The atom missing the electron will have a net positive charge, and it                                 is called an ion and said to be ionized .  In our current quantum mechanical understand, electrons do not orbit the nucleus at very                           specific distances associated with very specific energies. In quantum mechanics, electrons                     exist as a cloud surrounding the nucleus where they are both wave and particle                           simultaneously. Statistically, the electrons will, on average, be the distances away from the                         nucleus as described in the Bohr model. So, while not our current model, the Bohr model                               accurately describes the energies of the electrons, and this is the key factor to linking how                               photons, with specific energies dependent on wavelength, will interact with atoms.  

 

Figure 3. The Bohr Model of the atom. +Z represents the number of protons in the nucleus, which                                   defines the element (Z = 1 is hydrogen, Z=2 is helium, Z = is lithium, etc.). the gray orbits are the                                         electron orbitals, which all relate to the electron having a specific energy. The electron can                             change to a higher energy level if it absorbs a photon with the exact right amount of energy. The                                     electron cna change to a lower energy level if it emits a photon with the exact right amount of                                     energy, ΔE = h𝜈 (f in the figure).  

 

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1.5 Spectroscopy 

Spectroscopy describes how photons of light will interact with the matter. For atoms, this                           interaction will be between the electrons and light. In spectroscopy, the spectrum (plural:                         spectra) of light is measured, which is the intensity of radiation as a function of wavelength or                                 frequency. For this lab, we will be using wavelength. In other words, a spectrum is a measure                                 of how bright (intense) each wavelength of light is. This requires breaking the light up into its                                 component wavelengths, which is done with either a prism or a diffraction grating, and then                             observing and measuring how bright each wavelength is. 

Recall that the electrons in an atom can only exist in specific energy levels, or electron                               orbitals. An electron can either gain (absorb) or lose (emit) energy and through the exchange                             of a photon. An electron can absorb photons with specific energies and move to higher                             energy levels, and give off photons when they lose energy, but they must do so with exact                                 quantities of energy. These changes of one energy level to another are referred as electronic                             transitions. If the energy of the photon does not match the energy the electron needs to                               change energy levels, the photon will pass right through the atom without interacting. 

1.6 Spectra 

When light is broken into its component wavelength, or rather, observed as a spectrum,                           three different patterns are seen. If all wavelength of light are seen, although with some                             variation in intensity, the spectrum is a continuous spectrum. Hot, dense objects emit                         continuous spectra. If most of the wavelengths of light are seen, but with very specific                             wavelengths missing, the spectrum is an absorption spectrum, and the missing wavelengths                       are called absorption lines . A continuous source viewed through a cool gas will produce an                             absorption spectrum . If only very specific wavelengths of light are bright, and the rest of the                               wavelengths are absent, the spectrum is an emission spectrum , and the bright wavelengths                         are called emission lines. A hot, diffuse (very low-density) gas will produce an emission                           spectrum . Examples of what these three types of spectra look like using visible light are                             shown in Fig. 4. 

 

Figure 4. The three types of observed spectra: continuous, emission, and absorption. The bright                           lines in the emission spectrum are called emission lines. The dark lines in the absorption                             spectrum are called absorption lines. Every element has a unique set of emission and absorption                             lines making a spectrum a “fingerprint” of chemical composition. 

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What is the relationship between these three types of spectra? The answer to that is                             explained by how light interacts with matter. Hot, dense objects emit what astronomers                         called thermal radiation or continuous radiation. All wavelengths of light are present, and the                           intensity of each wavelength depends on the temperature of the object. Emission spectra                         and absorption spectra are a bit more complicated. The emission and absorption lines are                           created by electrons either moving to lower energy levels and emitting photons of specific                           energies (and therefore specific wavelengths), or moving to higher energy levels by absorbing                         photons of specific wavelengths. The energy change, ΔE = hc/𝜆 , of those emitted or absorbed                             photons corresponds to the change in energy required to move the electron from one energy                             level to another. 

When viewing the emission, or absorption, spectrum of an element, the light present, or                           absent, represents the energy levels of the atoms. Each atom has its own balance of positive                               and negative charges, the electron energies levels are unique. So each element has different ,                             emission, or absorption, spectra, which allows for a unique identification of an element. In                           this way, spectra are like fingerprints for the elements. 

Figure 5 shows the emission elements for several elements on the periodic table. As can be                               seen in the figure, each element has a unique set of spectral lines. The unique lines for each                                   element allows astronomers to determine the chemical composition of astronomical objects                     by simply observing the light from them as a spectrum. With this technique, astronomers                           have determined the chemical composition of planetary atmospheres, stars, nebulae of all                       kinds, supernovae, galaxies, etc. In turn, this information has given us insight into how all the                               elements on the periodic table form, and how the chemistry of the universe is always                             evolving. 

   

Figure 5. Emission spectra for several elements on the periodic table. Each element has a unique set of emission lines or spectral “fingerprints.” 

1.7 The Hydrogen Atom 

The simplest atom, hydrogen, element number one, is also the most abundant element in the                             universe. In its simplicity, physicists have been able to work out exactly what the electron                             

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energy levels are for the hydrogen atom. The Bohr model for the hydrogen atom with the                               lowest energy levels depicted is shown in Figure 6. Notice that the energy required to go from                                 the ground state (n = 1) to the first excited state (n = 2) is the largest energy difference (ΔE12 =                                         10.2 eV) between two adjacent levels. Each move to a higher energy level requires a little bit                                 less energy. The most energy an electron can transition in the hydrogen atom is the from the                                 ground state through all the excited states to ionization. For hydrogen, this ionization energy                           is 13.6 eV. 

 

Figure 6. The Bohr model for hydrogen. The energy differences between the ground state and the                               next highest state are shown for n = 1 to n = 4. The ionization energy (n = 1 all the way to n = ∞, or                                                     removed from the atom) for hydrogen is E = 13.6 eV. Two of the names series of hydrogen, the                                     Lyman and Balmer series, are shown with some of the photon wavelengths listed. 

Knowing the energy of each energy-level of hydrogen, it is possible to work out what                             wavelengths will be absorbed or emitted as an electron transitions from one energy level to                             another. This is true for moving to higher energy levels (to higher excited states) via the                               absorption of the photon or to lower energy levels (to lower excited states) through the                             emission of a photon. The wavelength of a photon moving from the n1 to the n2 state is given                                      by the Rydberg formula for hydrogen: 

 

= λ R( ( 1n2

1− 1n2

2))−1

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where λ is the wavelength of the photon, n1 is the lower energy state and n2 is the higher                                     energy state. R is the Rydberg constant, which has a value of 1.097E-7 m -1. Since R is inverted                                   and we are interested in the nanometer scale, let’s pull it out of the inversion and use a value                                     of R -1 = 91.2 nm. 

= 1.2 nm λ 9 ( 1n2

1− 1n2

2)−1

 

Certain electronic transitions for the hydrogen atom get special names. Any transition into or                           out of the ground state (n = 1) is referred to a Lyman transition. All together, all n = 1 to                                         another state or another state back down to n =1 are referred to as the Lyman Series. The                                   lowest energy transition in Lyman series would between the n = 1 to n = 2 state (in either                                     absorption or emission) with a change in energy of 10.2 eV. Using E[eV] = 1240/𝜆[nm] , this                               wavelength of the absorbed or emitted photon can then be calculated to be 121.6 nm. This                               transition is called Lyman alpha ( L 𝞪). The next highest energy transition would be between                           the n = 1 and n = 3 state, and it is called Lyman beta (L𝜷). The next, Lyman gamma (L𝜸) and so                                             on and so forth proceeding through the Greek alphabet. The highest energy Lyman transition                           is from the ground state to ionization (ΔE = 13.6 eV), which comes out to be a wavelength of                                     91.2 nm, which is the wavelength coefficient in the Rydberg formula. So, all Lyman series                             wavelengths are between 91.2 nm - 121.6 nm, which are all ultraviolet photons. 

Another famous series of electronic transitions for hydrogen is the Balmer Series. Like the                           Lyman series, this series is defined by any transition into or out of the first excited state (n =                                     2). Note that the transition from the ground to first excited state is a Lyman transition and                                 therefore not part of the Balmer series. The lowest energy Balmer transition is between n = 2                                 and n = 3, which has an energy difference of about 1.9 eV. This works out to a wavelength of                                       656.3 nm in the red part of the visible spectrum. Instead of this line being called Balmer alpha,                                   it is instead called hydrogen alpha (H 𝞪). The Balmer series transitions called the hydrogen                           lines because they were the first spectral lines observed for hydrogen due to them all being                               visible light photons. The Balmer series naming proceeds just as it did with the Lyman series,                               and the highest energy transition from n = 2 to ionization has a change in energy of 3.4 eV,                                     giving a wavelength of 1240/3.4 = 364.6 nm at the violet end of the visible spectrum. 

1.8 The dance of electrons in an atom 

We have been discussing how an electron in atom can transition between energies levels                           through the exchange of a photon: either emitting a photon to give up energy or absorbing a                                 photon to gain energy. The electron will only absorb or emit photons with the correct amount                               of energy, and hence correct wavelength, to transition from one level to another. All other                             photons do not generally interact with the atom.  

Using the hydrogen atom, let’s consider an electron that gets excited to the n = 3 state.                                 Electrons do not like being excited, and therefore will rapidly move back down to the ground                               state (n = 1) by emitting photons to get back to its preferred lowest energy state. There are                                   multiple paths the electron can take to get back to the ground state. It can transition directly                                 

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from the n = 3 to the n = 1 state by emitting a photon with energy E = 10.2 + 1.9 = 12.1 eV (𝜆 =                                                     1240/12.1 = 102.5 nm). In this case, the hydrogen atom absorbed an ultraviolet photon with E                               = 12.1 eV (𝜆 = 102.5 nm), and then re-emitted a photon with the exact same energy and                                   wavelength. The re-emission, however, is done so in a random direction, so this process is                             one form of scattering of light. Instead of a direct transition to back to the ground state, the                                   electron could have transitioned from the n = 3 to the n = 2 state and then from the n = 2 to                                             the n = 1 state. In this case, the hydrogen atom absorbs a single photon with energy E = 12.1                                       eV, but emits two different photons: one of energy E = 1.9 eV (𝜆 = 656.3 nm) and one of E = 10.2                                             eV (𝜆 = 121.6 nm). This case of absorbing a photon of one energy (wavelength) and emitting                                 multiple photons (multiple wavelengths) with energies that add up to the same energy is                           called fluorescence. A slightly more complicated example is how an electron in a hydrogen atom can go from the n                                   = 4 state back to the ground state (n = 1). Figure 7 shows all FOUR of the pathways this                                       electron can take to get back to the ground state with all SIX possible different photons that                                 can be emitted over all possible pathways. You can use the Rydberg formula in Section 1.7 to                                 calculate the wavelengths for each of the transitions, and then use the equation relating                           wavelength of light to energy to determine the energy of the transition. It is through this                               method that scientists were able to measure the energy structure of the hydrogen atom and                             test the predictions of the emerging atomic theory and quantum mechanical theory. 

 

Figure 7. All the possible electron pathways an electron can take when transitioning from the n = 4 (3rd Excited state) to the n = 1 (Ground State). There are four paths the electron could take: 4-3-2-1 4-3-1 4-2-1 4-1. Over all pathways, there are six possible photons that could be released. The equations in this lab give a way of calculating the wavelengths and energies of those photons. 

    

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2. Lab Activity 1   Use the Vernier Spectroscopy & LoggerPro3 setup to collect digital spectra.  If Vernier LoggerPro3 isn’t already running on your laptop, double-click on the icon on the                             desktop. The software should open and automatically load an intensity vs. wavelength graph.                         When ready to collect spectra, click the collect button to begin.   Cycle through the 6 elements in the carousel. Be careful not to kink the fiber optic cable. Use                                   

the Examine tool to determine the emission wavelength. Record the wavelengths which                       have the highest intensity.   Record in Table 4.2.1.   

 3. Lab Activity 2  

 

Rotate through the spectroscopes, sketching the spectra and recording the wavelength of the brightest three emission lines. Use the spectra from Lab Activity 1 to identify the unknown elements. To maximize the life of the discharge bulbs, turn them on for 30 seconds, then off for 30 seconds. Record in Table 4.2.2.   

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Spectroscopy Name: ____________________________________  4. Analysis and Summary Exercises  4.1 Pre-lab Reading Questions – [Total pts for additional questions]  4.1.1 - What is the electromagnetic spectrum? List at least three of the named regions of the EM spectrum.   4.1.2 - At what speed does light travel in a vacuum? Does this value change for different colors?   4.1.3 - Which has more energy per photon, radio or gamma rays?   4.1.4 - Why are the spectra of elements considered to be “fingerprints” that astronomers can use to determine the chemical composition of astronomical objects?   4.1.5 - Are electrons allowed to exist with any energy around an atom, or are they restricted to specific energies?     

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 4.2 In-class Lab Questions – [Total pts for additional questions] 

4.2.1 - Cycle through the elements in the carousel, and record the wavelengths of the three most intense emission lines.  

Carousel Position  Most Intense Wavelengths  Element ID 

1 

_____________________  _____________________  _____________________  

Argon (Ar) 

2 

_____________________  _____________________  _____________________  

Carbon Dioxide (CO2) 

3 

_____________________  _____________________  _____________________  

Hydrogen (H) 

4 

_____________________  _____________________  _____________________  

Helium (He) 

5 

_____________________  _____________________  _____________________  

Nitrogen (N) 

6 

_____________________  _____________________  _____________________  

Neon (Ne) 

7 

_____________________  _____________________  _____________________  

Air (N 2 O2 Ar) 

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 4.2.2 - Visit each spectroscope and sketch the spectrum of each element. Record the                           wavelength of the three brightest emission lines, and use the information from Table 4.2.1 to                             identify the element by recording the element symbol (e.g., H for hydrogen, He for helium,                             etc.) in the Element column. 

 

Element  Spectra  Wavelengths 

 

 

____________  ____________  ____________  

 

 

____________  ____________  ____________  

 

 

____________  ____________  ____________  

 

 

____________  ____________  ____________  

 

 

____________  ____________  ____________  

 

 

____________  ____________  ____________  

 

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 Name: 

Lab TA 

Lab Section: 

 4.3 Student Worksheet – [Total pts for additional questions]  

1. Rank the listed parts of the electromagnetic spectrum in order from: 

Microwaves  Gamma Rays  Infrared Light  Ultraviolet Light 

 a) Shortest to Longest WAVELENGTH 

 

Shortest  ----------------------------------------------->  Longest 

       

 b) Lowest to Highest FREQUENCY 

 

Lowest  ----------------------------------------------->  Highest 

       

 c) Lowest to Highest ENERGY 

 

Lowest  ----------------------------------------------->  Highest 

       

 2. Consider a visible photon and an X-ray photon. 

a. Which photon has the longest (largest) wavelength [or are they the same]?  

b. Which photon has the highest (largest) energy [or are they the same]?  

c. Which photon travels fastest in a vacuum [or are they the same]?    

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3. A household microwave oven will cook your food with microwaves with a frequency,  𝜈 = 2,450 Mhz. 

a. What is this frequency in Hertz [Hz]?    

b. Use your answer from (a) and the equation relating the speed of light, wavelength, and frequency to calculate the wavelength in meters of this light.    

4. Green light is in the middle of the visible portion of the electromagnetic spectrum. It has a wavelength of about 550 nm. 

a. What is the wavelength of green light in meters?     

b. Use your answer from (a) and the equation relating the speed of light, wavelength, and frequency to calculate the frequency in Hz and green light.     

5. A helium atom has two electrons. The ionization energy to remove one of the electrons from helium is E = 24.6 eV. What wavelength photon does this energy correspond to? In what part of the electromagnetic spectrum is that photon (See Figure 1)?       

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 6. Below is a spectrum for the element hydrogen.  

  

a. What type of spectrum is displayed(emission, absorption, or continuum)?   

b. What spectral series of hydrogen is displayed?   

c. List the electron transitions for those lines (n = ? to ?). Label which is which in your answer.    

d. Use the Rydberg formula given in the lab to calculate the wavelengths of H-alpha, H-beta, and H-gamma.     

7. Describe how the spectra of elements serve as “fingerprints” that allow astronomers to determine the composition of astronomical objects.         

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8. Using the following elemental spectra, answer the following questions: 

  

a. Which mixture(s) contain hydrogen gas?   

b. Mixture A is a mixture of what gasses?   

c. Mixture B is a mixture of what gasses?   

d. Mixture C is a mixture of what gasses?      

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 9. Calculate the wavelengths for all possible photons in the  

Lyman (into or out of n = 1),  Balmer (into or out of n = 2),  Paschen, (into or out of n= 3), and Brackett (into or out of n = 4) 

series for hydrogen from n = 5. You will need to use the Rydberg formula given in this lab to complete the table. (A spreadsheet may be useful.) 

 Wavelengths 

  Lyman  Balmer  Paschen  Brackett 

n = 5         

n = 4        _____________ 

n = 3      _____________  _____________ 

n = 2    _____________  _____________  _____________ 

  

   

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 10. Using Figure 7 as an example to answer the following: 

a. Draw out all the pathways an electron in a hydrogen atom can go from the n = 5 to the ground state n = 1.                  

b. How many unique pathways can it take?   

c. How many different photons can be emitted over all transitions from n = 5 to n = 1?   

d. Use the wavelengths to calculate the energy of each photon.  

Energies 

  Lyman  Balmer  Paschen  Brackett 

n = 5         

n = 4        _____________ 

n = 3      _____________  _____________ 

n = 2    _____________  _____________  _____________ 

 

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