Emission and absorption spectra

Emission spectra

You have learnt previously about the structure of an atom. The electrons surrounding the atomic nucleus are arranged in a series of levels of increasing energy. Each element has its own distinct set of energy levels. This arrangement of energy levels serves as the atom's unique fingerprint.

In the early 1900s, scientists found that a liquid or solid heated to high temperatures would give off a broad range of colours of light. However, a gas heated to similar temperatures would emit light only at certain specific colours (wavelengths). The reason for this observation was not understood at the time.

Scientists studied this effect using a discharge tube.

Figure 1: Diagram of a discharge tube. The tube is filled with a gas. When a high enough voltage is applied across the tube, the gas ionises and acts like a conductor, allowing a current to flow through the circuit. The current excites the atoms of the ionised gas. When the atoms fall back to their ground state, they emit photons to carry off the excess energy.

A discharge tube (Figure 1) is a glass gas-filled tube with a metal plate at both ends. If a large enough voltage difference is applied between the two metal plates, the gas atoms inside the tube will absorb enough energy to make some of their electrons come off i.e. the gas atoms are ionised. These electrons start moving through the gas and create a current, which raises some electrons in other atoms to higher energy levels. Then as the electrons in the atoms fall back down, they emit electromagnetic radiation (light). The amount of light emitted at different wavelengths, called the emission spectrum, is shown for a discharge tube filled with hydrogen gas in Figure 2 below. Only certain wavelengths (i.e. colours) of light are seen as shown by the thick black lines in the picture.

Figure 2: Diagram of the emission spectrum of hydrogen in the visible spectrum. Four lines are visible, and are labelled with their wavelengths. The three lines in the 400–500 nm range are in the blue part of the spectrum, while the higher line (656 nm) is in the red/orange part.

Eventually, scientists realised that these lines come from photons of a specific energy, emitted by electrons making transitions between specific energy levels of the atom. Figure 3 shows an example of this happening. When an electron in an atom falls from a higher energy level to a lower energy level, it emits a photon to carry off the extra energy. This photon's energy is equal to the energy difference between the two energy levels. As we previously discussed, the frequency of a photon is related to its energy through the equation . Since a specific photon frequency (or wavelength) gives us a specific colour, we can see how each coloured line is associated with a specific transition.

Figure 3: In this diagram are shown some of the electron energy levels for the hydrogen atom. The arrows show the electron transitions from higher energy levels to lower energy levels. The energies of the emitted photons are the same as the energy difference between two energy levels. You can think of absorption as the opposite process. The arrows would point upwards and the electrons would jump up to higher levels when they absorb a photon of the right energy.

Visible light is not the only kind of electromagnetic radiation emitted. More energetic or less energetic transitions can produce ultraviolet or infrared radiation. However, because each atom has its own distinct set of energy levels (its fingerprint!), each atom has its own distinct emission spectrum.

Absorption spectra

As you know, atoms do not only emit photons; they also absorb photons. If a photon hits an atom and the energy of the photon is the same as the gap between two electron energy levels in the atom, then the electron can absorb the photon and jump up to the higher energy level. If the atom has no energy level differences that equal the incoming photon's energy, it cannot absorb the photon, and can only scatter it.

Using this effect, if we have a source of photons of various energies we can obtain the absorption spectra for different materials. To get an absorption spectrum, just shine white light on a sample of the material that you are interested in. White light is made up of all the different wavelengths of visible light put together. In the absorption spectrum, the energy levels corresponding to the absorbed photons show up as black lines because the photons of these wavelengths have been absorbed and don't show up. Because of this, the absorption spectrum is the exact inverse of the emission spectrum. Look at the two figures below. In Figure 4 you can see the emission lines of hydrogen. Figure 5 shows the absorption spectrum. It is the exact opposite of the emission spectrum! Both emission and absorption techniques can be used to get the same information about the energy levels of an atom.

Figure 4: Emission spectrum of Hydrogen.

Figure 5: Absorption spectrum of Hydrogen.

Example 1: Absorption

Question

I have an unknown gas in a glass container. I shine a bright white light through one side of the container and measure the spectrum of transmitted light. I notice that there is a black line (absorption line) in the middle of the visible red band at 642 nm. I have a hunch that the gas might be hydrogen. If I am correct, between which 2 energy levels does this transition occur? (Hint: look at Figure 3 and the transitions which are in the visible part of the spectrum.)

Answer

What is given and what needs to be done?

We have an absorption line at 642 nm. This means that the substance in the glass container absorbed photons with a wavelength of 642 nm. We need to calculate which 2 energy levels of hydrogen this transition would correspond to. Therefore we need to know what energy the absorbed photons had.

Calculate the energy of the absorbed photons

(1)

The absorbed photons had energy of 3,1 × 10⁻¹⁹

Find the energy of the transitions resulting in radiation at visible wavelengths

Figure 3 shows various energy level transitions. The transitions related to visible wavelengths are marked as the transitions beginning or ending on Energy Level 2. Let's find the energy of those transitions and compare with the energy of the absorbed photons we've just calculated.

Energy of transition (absorption) from Energy Level 2 to Energy Level 3:

(2)

Therefore the energy of the photon that an electron must absorb to jump from Energy Level 2 to Energy Level 3 is 3,1 × 10⁻¹⁹ J. (NOTE: The minus sign means that absorption is occurring.)

This is the same energy as the photons which were absorbed by the gas in the container! Therefore, since the transitions of all elements are unique, we can say that the gas in the container is hydrogen. The transition is absorption of a photon between Energy Level 2 and Energy Level 3.

Colours and energies of electromagnetic radiation

We saw in the explanation for why the sky is blue that different wavelengths or frequencies of light correspond to different colours of light. The table below gives the wavelengths and colours of light in the visible spectrum:

We also know that the energy of a photon of light can be found from:

(3)

Therefore if we know the frequency or wavelength of light, we can calculate the photon's energy and vice versa.

Discharge lamps (sometimes incorrectly called neon lights) use the spectra of various elements to produce light of many colours.

Click to Run

Discharge lamps

Example 2: Colours of light

Question

A photon of wavelength 500 nm is emitted by a traffic light.

1. What is the energy of the photon?

2. What is the frequency of the photon?

3. Use Table 6 to determine the colour of the light.

Answer

What information is given and what do we need to find?

We are given and we need to find the photon's energy, frequency and colour.

Use the equation to find the photon's energy

(4)

The energy of the photon is 3,98 × 10⁻¹⁹ J.

We know the energy of the photon, now we can use to solve for the frequency

(5)

The frequency of the photon is 6 × 10¹⁴ Hz.

Use the table to find the colour of light

The wavelength given in the question is 500 nm. We can see in the table that green light has wavelengths between 492 – 577 nm. Therefore 500 nm is in this range so the colour of the light is green.

Example 3: Colours and energies of light

Question

I have some sources which emit light of the following wavelengths:

1. 400 nm,

2. 580 nm,

3. 650 nm,

4. 300 nm.

What are the colours of light emitted by the sources (see Table 6)? Which source emits photons with the highest energy and which with the lowest energy?

Answer

What information is given, and what do we need to do?

Four wavelengths of light are given and we need to find their colours.

We also need to find which colour photon has the highest energy and which one has the lowest energy.

To find the colours of light, we can compare the wavelengths to those given in Table 6

1. 400 nm falls into the range for violet light (390 – 455 nm).

2. 580 nm falls into the range for yellow light (577 – 597 nm).

3. 650 nm falls into the range for red light (622 – 780 nm).

4. 300 nm is not shown in the table. However, this wavelength is just a little shorter than the shortest wavelength in the violet range. Therefore 300 nm is ultraviolet.

To find the colour of the light whose photons have the highest and lowest energies respectively, we need to calculate the energies of all the photons

We know

For 400 nm:

(6)

For 580 nm:

(7)

For 650 nm:

(8)

For 300 nm:

(9)

Therefore, the photons with the highest energy are the ultraviolet photons.

The photons with the lowest energy are from light which is red.

Applications of emission and absorption spectra

The study of spectra from stars and galaxies in astronomy is called spectroscopy. Spectroscopy is a tool widely used in astronomy to learn different things about astronomical objects.

Global warming and greenhouse gases

The sun emits radiation (light) over a range of wavelengths which are mainly in the visible part of the spectrum. Radiation at these wavelengths passes through the gases of the atmosphere to warm the land and the oceans below. The warm earth then radiates this heat at longer infrared wavelengths. Carbon-dioxide (one of the main greenhouse gases) in the atmosphere has energy levels which correspond to the infrared wavelengths which allow it to absorb the infrared radiation. It then also emits at infrared wavelengths in all directions. This effect stops a large amount of the infrared radiation getting out of the atmosphere, which causes the atmosphere and the earth to heat up. More radiation is coming in than is getting back out.

Therefore increasing the amount of greenhouse gases in the atmosphere increases the amount of trapped infrared radiation and therefore the overall temperature of the earth. The earth is a very sensitive and complicated system upon which life depends and changing the delicate balances of temperature and atmospheric gas content may have disastrous consequences if we are not careful.

Investigation 2: The greenhouse effect

In pairs try to find the following information (e.g. in books, on the Internet) and report back to the class in a 5 minute presentation which includes the following:

1. What other gases besides carbon dioxide are responsible for the greenhouse effect?

2. Where do greenhouse gases come from? (are they human-made or natural?)

3. Investigate one serious side-effect which could arise if the earth's temperature were to go up significantly. Present some ways in which this effect could be avoided.

Exercise 1: Emission and absorption spectra

Problem 1:

Explain how atomic emission spectra arise and how they relate to each element on the periodic table.

Answer 1:

Atomic emission spectra arise from electrons dropping from higher energy levels to lower energy levels within the atom, photons (light packets) with specific wavelengths are released. The energy levels in an atom are specific/unique to each element on the periodic table therefore the wavelength of light emitted can be used to determine which element the light came from.

Problem 2:

How do the lines on the atomic spectrum relate to electron transitions between energy levels?

Answer 2:

The lines on the atomic spectrum relate to electron transitions between energy levels, if the electron drops an energy level a photon is released resulting in an emission line and if the electron absorbs a photon and rises an energy level an absorption line is observed on the spectrum.

Problem 3:

Explain the difference between atomic absorption and emission spectra.

Answer 3:

The difference between absorption and emission spectra are that absorption lines are where light has been absorbed by the atom thus you see a dip in the spectrum whereas emission spectra have spikes in the spectra due to atoms releasing photons at those wavelengths.

Problem 4:

Describe how the absorption and emission spectra of the gases in the atmosphere give rise to the Greenhouse Effect.

Answer 4:

The following needs to be in your answer: in what wavelength range the sunlight reaches the earth, the absorption of the sunlight and the re-radiation as infrared light, and finally the scattering of the infrared light by the carbon-dioxide and how this scattering contributes to the Greenhouse Effect.

Problem 5:

Using Table 6 calculate the frequency range for yellow light.

Answer 5:

The frequency range of yellow light is . (1 THz = 10¹² Hz)

Problem 6:

What colour is the light emitted by hydrogen when an electron makes the transition from energy level 5 down to energy level 2? (Use Figure 3 to find the energy of the released photon.)

Answer 6:

The colour of light emitted at 423 nm is violet.

Problem 7:

I have a glass tube filled with hydrogen gas. I shine white light onto the tube. The spectrum I then measure has an absorption line at a wavelength of 474 nm. Between which two energy levels did the transition occur? (Use Figure 3 in solving the problem.)

Answer 7:

This energy interval corresponds to a transition from energy level 4 to energy level 2.