Directions: After students have had a chance to review the article “Mosses tell story of retreating ice,” lead a classroom discussion based on the questions that follow.

PHYSICAL AND CHEMICAL SCIENCES

Discussion questions:

1. What are isotopes, and what are the isotopes of carbon? What carbon isotopes are radioactive?

Isotopes are atoms of the same element with different masses — they have the same numbers of protons and same numbers of electrons, but different numbers of neutrons. Most of the naturally occurring carbon on Earth is carbon-12 or ¹²C (its nucleus contains 6 protons and 6 neutrons). Approximately 1 percent is carbon-13 or ¹³C (its nucleus contains 6 protons and 7 neutrons). Both of those carbon isotopes are stable — they do not radioactively decay to become another element. If certain other elements are exposed to radiation, they can temporarily form other carbon isotopes that are radioactive. Carbon-11 or ¹¹C (its nucleus contains 6 protons and 5 neutrons) decays with a half-life of approximately 20 minutes to become stable boron-11 or ¹¹B (its nucleus contains 5 protons and 6 neutrons). Carbon-14 or ¹⁴C (its nucleus contains 6 protons and 8 neutrons) decays with a half-life of approximately 5,730 years to become nitrogen-14 or ¹⁴N (its nucleus contains 7 protons and 7 neutrons).

2. What is beta decay? Write the decay equation for carbon-14.

Beta particles are electrons (which have negative electric charge) and positrons (the positively charged antimatter version of an electron). In beta-minus decay, a neutron turns into a positively charged proton plus an electron (along with a neutral particle called an anti-neutrino). In beta-plus decay, a proton turns into a neutron plus a positron (and a neutrino). Beta decay occurs when an atom trades a neutron for a proton or vice versa, in order to reach a more stable, lower-energy state.

The beta-minus decay equation for carbon-14 is: ¹⁴C →¹⁴N + e^– (and an anti-neutrino)

3. How is carbon-14 formed in the atmosphere?

High-energy cosmic rays from the sun or other sources in space hit atoms in the upper atmosphere, knocking loose neutrons. Most of the atmosphere is made of ¹⁴N (its nucleus contains 7 protons and 7 neutrons). If a neutron generated by a cosmic ray knocks a proton out of ¹⁴N and takes its place, carbon-14 (its nucleus contains 6 protons and 8 neutrons) is formed:

            ¹⁴N + n⁰→ ¹⁴C + p⁺

Carbon in the atmosphere combines with oxygen to form carbon dioxide or CO₂. Roughly 1×10^-12 of the carbon in atmospheric CO₂ is carbon-14.

4. How does carbon dating work?

Living organisms acquire carbon from atmospheric CO₂ either directly for plants or indirectly for other organisms (herbivorous animals eat plants that have acquired atmospheric carbon, and carnivorous animals eat herbivorous animals that have eaten plants that acquired atmospheric carbon). Approximately 1 atom out of every 10¹² newly acquired carbon atoms is carbon-14. As long as an organism is living and exchanging carbon with the environment, the percentage of carbon-14 in an organism should remain approximately equal to that of the environment. Carbon-14, which has a half-life of approximately 5,730 years, decays at a rate of about 13.5 atoms/minute per gram of total carbon. After the organism has been dead for about 5,730 years, it should contain 1/2¹ = 1/2 of that original amount of carbon-14. After the organism has been dead for 11,460 years (5,730 x 2), it should contain 1/2² = 1/4 of the original amount of carbon-14. After the organism has been dead for 17,190 years (5,730 x 3), it should contain 1/2³ = 1/8 of the original amount of carbon-14. And so forth.

5. How is carbon-14 measured?

For younger and/or larger samples that contain more carbon-14, the carbon-14 content can generally be measured by a radiation counter to directly detect beta decay of carbon-14 into nitrogen-14. For older and/or smaller samples with very little carbon-14, a mass spectrometer can be used, distinguishing the charge and mass of different ions vaporized from the sample.

Extension prompts:

6. What are the limitations of carbon-14 dating?

After 45,840 years (5,730 x 8), only 1/2⁸ = 1/256 of the original amount of carbon-14 is left. Because the original amount of carbon-14 was very small to begin with, it is very difficult to carbon-date an object that is older than 40,000–50,000 years. Also, carbon dating is only useful for determining the age of something that was once alive and absorbing carbon. That is great for remains of humans, animals and plants, as well as human tools that were made from plants or animals. However, it is not useful for stone or metal tools, rocks and minerals, and other objects that were never alive.

7. What other radioactive decays are useful for dating objects?

Longer-lived isotopes can be used to date rocks and estimate the age of Earth, the moon, meteorites and other objects that are older than 50,000 years. One useful isotope is potassium-40, which has a half-life of approximately 1.25 billion years. Potassium-40 beta-decays to calcium-40. It can also decay through a process called electron capture into argon-40. Argon-40 is a gas that easily escapes from hot molten rock, but not cooled solid rock. So newly formed igneous rocks should have virtually no argon-40, and older igneous rocks can be dated by how much of their potassium-40 has decayed to trapped argon-40.

Another useful isotope is uranium-238, which undergoes a series of several decays to ultimately become lead-206. Uranium-238 has a half-life of approximately 4.47 billion years. And radioactive isotope uranium-235, also undergoes a series of several decays to ultimately become lead-207. Uranium-235 has a half-life of approximately 710 million years.

BIOLOGICAL AND EARTH SCIENCES

Discussion questions:

1. How do plants use photosynthesis to incorporate atmospheric carbon?

The chloroplasts in plant cells absorb energy from sunlight (using chlorophyll molecules), use that energy to break up water (H₂O) and atmospheric carbon dioxide (CO₂) and combine their components one step at a time to produce sugars (containing C, H and O) and oxygen (O₂). In further steps, plant cells use those sugars to form a wide variety of other biological molecules. Those sugars and the biological molecules made from them are thus built from atmospheric carbon.

2. What are the major greenhouse gases and why are they called greenhouse gases? How has the level of carbon dioxide changed in recent history?

Carbon dioxide, methane, water vapor, nitrous oxide and ozone are all greenhouse gases. They are called greenhouses gasses because they trap heat in Earth’s atmosphere, similar to how a greenhouse traps heat. Short wavelengths of sunlight enter through the atmosphere and are absorbed by Earth’s surface. Some of the sunlight is re-emitted by Earth as thermal radiation, or heat. Greenhouse gasses in the atmosphere then absorb some of that heat and reflect some back to Earth’s surface, so Earth gets warmer. Atmospheric carbon dioxide has increased from approximately 300 to over 400 parts per million (ppm) over the last century.

3. How has the global average temperature and sea level changed in recent history?

Global average temperature has risen by about 1° Celsius, or about 1.8° Fahrenheit, over the last century. As a result, global ice melts and ocean temperatures warm (water expands as it becomes warmer), contributing to sea level rise. Sea levels have risen by about 20 centimeters over the last century.

Extension prompts:

4. How have human activities affected the climate? How does the speed of the environmental changes today contrast the speed of changes in the past?

Most changes in Earth’s climate have occurred slowly over millions of years, allowing species to adapt. But greenhouse gas emissions from human activities have increased the rate of climate change over the last century. Millions of years ago, relatively quick, drastic changes in the environment resulted in mass extinctions. There have been five mass extinctions in Earth’s history. During the last mass extinction event, 66 million years ago, about 75 percent of all species disappeared, including non-avian dinosaurs.

ENGINEERING AND EXPERIMENTAL DESIGN

Discussion questions:

1. What types of sensors could detect radiation from carbon-14, and how do they work?

A Geiger-Mueller tube is filled with a gas between high-voltage electrodes. If a beta particle from carbon-14 (or some other type of radiation) passes through the gas, it will ionize some of the atoms in the gas, conducting current between the electrodes and giving an electrical signal. 

A scintillation material, such as zinc sulfide, emits light when a beta particle (or other type of radiation) passes through it. The radiation boosts electrons in the material to higher energy levels, and they give off photons when they drop back down to lower energy levels.

A junction diode, or semiconductor detector, senses electrical signals produced when beta particles (or other type of radiation) deposit enough energy to raise electrons in the semiconductor to higher energies.

2. What types of sensors could detect carbon-14 directly (without measuring its radiation), and how do they work?

A mass spectrometer can be used to directly detect carbon-14. Carbon-14, carbon-12 and other atoms from a sample can be vaporized, fully ionized (their charge will depend on the number of protons they contain) and accelerated to a known high energy state in a small particle accelerator that creates brief pulses. The pulsed beam of ionized atoms can be passed through a magnetic field of known strength. By the Lorentz force, the trajectories of ions with different charges and different masses will be bent by different amounts. If all the ions have the same amount of energy, but different masses, they will also have different speeds — smaller ions with less mass will have higher velocities and reach their destination more quickly, whereas larger ions with more mass will have lower velocities and reach their destination more slowly. If an array of sensors detects where and when the ions from the beam arrive on the other side of the magnetic field, the charge (number of protons) and mass (number of protons + neutrons) of each ion can be determined.

Extension prompts:

3. How might you design a portable carbon-14 dating device that could rapidly determine the age of a fragile, valuable object such as an ancient manuscript?

Student answers will vary, but students should consider nondestructive measurement of beta particles from carbon-14 (and estimating how much total carbon is in the object) versus destructive measurement of carbon-14 in a mass spectrometer (or how to minimize how much of a sample is needed for a mass spectrometer).