(eV). The value can be multiplied by 1.602 × 1019 to give the value in joules.
This equation approximates to:
(3.5)
The value, 13.6, in this equation is also known as the Rydberg unit of energy(Ry).
Taking the formula we have just seen (Eq. (3.5)), we can observe that the energy needed to make an electron jump from one energy level to another (or the energy of a photon given off when an electron drops from one energy level to another) is therefore given by:
(3.6)
where n1 and n2 are the energy levels and n1 < n2.
3.14.1 The Special Case of the Hydrogen Atom
The hydrogen atom, which is of course a common constituent of the Universe, is a special case, since its mass number, the value of Z, is 1. This leads to the general formula for the energy required for an electron to change energy levels in this atom as:
(3.7)
The wavelength of light that would be emitted or taken up by a transition between these two energy levels is therefore also given by:
(3.8)
This equation can also be expressed in a different way, known as the Rydberg formula (for hydrogen):
(3.9)
where the Rydberg constant (R∞) is equal to Ry/hc and has a value of 1.097 × 107 m−1.
A special case of this equation is when hydrogen is ionized. In this case, the electron is completely removed from the atom, so that n2 = ∞. If the electron is in the ground state (i.e. n1 = 1), then the energy required for ionization is equal to Ry eV or 13.6 eV.
3.14.2 Uses for Astrobiology
The implications of the above equations and ideas in relation to astrobiology can now be explained.
When a collection of hot gases absorbs light, the electrons in its constituent gases jump energy levels and drop back down again, emitting light at discrete wavelengths. These give rise to emission spectra (Figure 3.25b). Each individual gas has a very characteristic emission spectrum that is a fingerprint, if you will, of its atomic structure, with lines arranged across the spectrum corresponding to the different energy levels of its electronic orbitals (Figure 3.25b). This emission spectrum can be used to identify the different gases in astronomical objects. These effects are pressure dependent, and at very high pressures, hot gases tend to produce continuous spectra without characteristic emission lines.
The detection of gases in the atmospheres of distant stars, beginning in the late nineteenth century, finally confirmed that distant stars are other suns. By characterizing these gases in stars of different colors and luminosities, it became possible to systematically categorize stars into different spectral types.
By contrast, if light travels through a collection of cold gases, the gases tend to absorb the light at the particular wavelengths corresponding to the energies needed to make electrons jump energy levels, dependent on the atomic structure of the individual gases. These create a characteristic absorption spectrum, essentially places in the spectrum where the light is “missing.” Absorption spectra from stars are characterized by very distinct lines in the spectrum called Fraunhofer lines, named after German optician Joseph von Fraunhofer (1787–1826). The temperature and density within a star affect the intensity of the lines, and so they can reveal information about the characteristics of a given star.
As we shall see later, absorption spectroscopy allows us to investigate the gaseous composition not just of stars, but also of planetary atmospheres, such as those of extrasolar planets. By collecting light from a star that has traveled through a planetary atmosphere, we can determine the gaseous composition of the atmosphere and seek gases that are signatures of life (Chapter 20).
We leave the summary of this last section to German physicist Gustav Kirchhoff (1824–1887) who listed, before the structure of the atom was understood, what are sometimes called the three laws of spectroscopy:
1 A hot solid object gives off a continuous spectrum (called a blackbody – we return to this in Chapter 9).
2 A hot gas, under low pressure, produces a bright-line or emission spectrum, which depends on the energy levels of the atoms in the gas.
3 A hot solid object surrounded by a cooler gas (e.g. light from a star passing through an exoplanet atmosphere) produces light with a spectrum (an absorption spectrum) that has gaps at discrete wavelengths depending on the energy levels of the atoms in the gas.
3.15 Conclusions
In this chapter, we explored the basic structure of matter relevant to astrobiology. We investigated the five major bonding types in matter. In each of these cases, we assessed the role of these bonding types in life with some examples. We saw how matter can be described in different states. By using simple phase diagrams, we can explain a variety of features of the physical characteristics of extraterrestrial environments and the conditions for life. We looked at some unusual states of matter, which although not part of living things certainly are an important part of the Universe and have consequences for the astronomical environment in which life resides. Finally, we investigated the principles of spectroscopy and how light interacts with matter in ways that are useful for scientists seeking to investigate the properties of gases in distant stars or planets. Equipped with this knowledge, we can now investigate how atoms and molecules are put together to make the basic molecules of life.
Questions for Review and Reflection
1 It is sometimes said that the existence of life requires covalent bonding. Discuss this statement.
2 Describe an example of the use of hydrogen bonding in living things. Why is this bonding type used in certain biological contexts and not others?
3 Explain the concept of an isotope with reference to atomic structure.
4 Why are solid metals not used in living things?
5 Draw a phase diagram of water and use it to explain some of the main features concerning the history of water on the surface of Mars. Use it to explain why the subsurface might be a better place to look for liquid water today.
6 There are extreme states of matter in the Universe, such as degenerate matter. Discuss whether you think a living thing could be constructed
