Creation and Destruction of Photons
THE BOHR ATOM
One of the most perplexing problems for earlytwentieth-century physicists was why the atom emits a discrete pattern of spectral lines. By 1913, when the structure of atoms was reasonably well known, Niels Bohr (1885-1962), a Danish physicist, proposed a theory for the structure of the simplest atom, hydrogen, whose one electron orbits around a proton. He suggested that the electron can occupy only a selected number of prescribed concentric orbits about the nucleus, rather than having an unlimited and unspecified orbital distance. Also, the electron normally resides in the lowest energy orbit, which is the one closest to the nucleus. Orbits representing higher levels of energy are increasingly farther from the nucleus. The diameter of the first orbit corresponds to the normal size of the hydrogen atom, about
10-8 centimeter in diameter.
When the atom absorbs energy, it is said to be excited, and the electron appears in one of the outer orbits, which have successively higher energies than the lowest orbit does. The electron's change (up or down) from one allowed orbit to another is called an electron transition. An atom in a gas may acquire the internal energy necessary to excite an electron by random thermal collisions with other gas atoms, collisions with subatomic particles such as free electrons, or absorption of a photon traveling through the gas.
Of all the photons striking the atom only those possessing an amount of energy equal to the energy difference between a higher energy orbit and the one in which the electron is located will be absorbed and excite the atom. For example, in the hydrogen atom it takes 10.2 electron volts, or 1.63 x 10-11 erg, of energy to raise the electron from its lowest energy orbit to the next higher energy orbit. Photons with energies below 10.2 electron volts will not be absorbed, and consequently the electron will not be excited. Photons with energies in excess of 10.2 electron volts cannot raise the electron to the second orbit, but they may, if they have the right amount of energy, excite the atom by lifting the electron to even higher energy orbits.
How long will an excited atom remain that way? If a gas atom is excited, then in about a hundredmillionth of a second it will rid itself of any energy in excess of that of the lowest energy orbit by emitting the energy in the form of one or more photons. Somewhat like a ball bouncing down a staircase, the electron will arop in succession into one or maybe several lower energy orbits on its way to the lowest energy level, where it can reside indefinitely. With each downward transition a photon of electromagnetic radiation is emitted. This photon represents the energy difference between the two orbits between which the electron makes the transition. The greater the energy difference, the greater is the amount of energy released in the form of a photon and, consequently, the shorter is the wavelength of the photon. Bohr was led to such a model for the atom as the most straightforward means of accounting for the discrete amounts of energy contained in photons. (Laboratory experiments had already shown that light really possessed the properties of a discrete phenomenon.)
Two examples from the countless electron transitions possible in the hydrogen atom are shown in Figure 4.14. Besides emitting energy spontaneously, an excited atom, before it can emit a photon, may collide with another atom in the gas and transfer energy to it as kinetic energy of motion. In this case no photon will be emitted.
SPECTRUM OF HYDROGEN ATOM
In addition to the model of the atom that represents it by its electron orbits, we can make a model using the energy of each allowed electron orbit. Such an energy-level model for hydrogen appears in Figure 4.16. The number of the energy levels corresponds in a one-to-one fashion with the number of the electron orbits. The distance between successive electron orbits increases with higher orbit numbers, but the differences in energy between successive orbits grows smaller as the orbit number increases.
Suppose a hydrogen atom is excited so that its electron is in the third energy level. Then it may de-excite directly to the ground state, emitting one photon. The photon would have a wavelength of 1026 angstroms,
which corresponds to the energy difference between these two orbits in the hydrogen atom. Or it may de-excite to the second energy level, emitting a photon with a wavelength of 6562 angstroms, and then de-excite from the second energy level to the ground state, emitting a photon with a wavelength of 1216 angstroms. The total energy emitted in both cases is the same, but the wavelengths that result and hence the spectral lines differ.
The hydrogen-line spectrum in the visible region, known as the Balmer series, is prominent in the absorption spectra of most stars. It arises from electron transitions originating on the second energy level of the atom. In the same way all the possible transitions from the ground level are known as the Lyman series, which is in the ultraviolet part of the electromagnetic spectrum. Those transitions from the third level up to higher energy levels are the Paschen series, which is in the infrared; and so on for the remaining series, whose lines appear in the far infrared on out to the microwave region of the spectrum.
Each series of spectral lines comes to a limit toward shorter wavelengths. The uppermost levels, representing the electron's highest energy orbits, crowd together toward a series limit, which represents the point beyond which the proton can no longer bind the electron to it. In this case the electron has been removed from the atom (it has been ionized) and is free to take on any energy.
If the electron is given enough energy, either by collision or absorption of a photon, it can escape the electrical attraction of the nucleus. The atom is then ionized and is in the form of a positive ion. The ionized hydrogen atom cannot absorb or reradiate energy in the form of discrete lines until it captures a free electron. It can execute the captu re because of the electrical force of attraction between the positively charged nucleus (the proton) and the negatively charged electron. Note that it converges toward its series limit at approximately 3646 angstroms.
SPECTRA OF OTHER ElEMENTS
In the Bohr atom, besides limits on the size of electron orbits, there is a limit to the number of electrons that may occupy a given orbit. These allowed orbits with a prescribed number of electrons in them are called electron shells.
In general, as one goes through the periodic table, electrons are added to balance the number of protons in the nucleus by filling the shells from the one closest to the nucleus outward. In hydrogen there is one electron in the innermost shell, which has room for a maximum of 2 electrons. Helium's 2 electrons fill, or close, the shell so that for the element lithium the third electron must start a new shell, which is the next innermost. In the second shell there is room for only 8 electrons; in the third, 18 electrons; in the fourth, 32; and so on.
Each element has a unique set of energy levels. Consequently, the wavelength of the spectral lines originating from electron transitions between various energy levels is also unique for each element-a clear fingerprint of the element.
The amount of energy needed to ionize an atom varies from one element to the next depending on the number and "position" of the electrons. For example, to remove the outermost electron from helium takes five times as much energy as it does to do the same for sodium. Also, for a given element each additional ionization takes more energy to free an electron from an inner orbit than from an outer one because the inner one is more tightly bound to the nucleus. Thus, with carbon as an example, it takes more than twice as much energy to remove the second electron than it does to remove the first; fou r times more for the third electron than the first; almost six times more for the fourth electron; thirty-five times more for the fifth electron; and a whopping forty-four times more for the innermost sixth electron than for the outermost first electron.
Multiple ionization of a carbon atom brings a corresponding readjustment of the energy levels because of the altered electrical attraction between the positive nucleus of the carbon atom and the reduced number of electrons. Altering the energy corresponding to each allowed orbit produces different spectral lines with each succeeding ionization of the carbon atom. So we see not only different wavelengths for absorption lines or emission lines between different unionized elements but for the same element a different spectrum after each ionization. That is, the spectrum of singly ionized carbon differs from the spectrum of neutral carbon; doubly ionized carbon differs from singly ionized; triply ionized differs from doubly ionized; and so on.
Using the properties of electromagnetic radiation, the atom's structure, the interaction between matter and energy, and spectrum analysis, astronomers have gained much information about the universe from the radiation it emits. And as we develop an even greater understanding of the nature of radiation-its formation, propagation, interaction with matter, and destruction-we can explore more deeply the dim sources in the outer reaches of the cosmos, almost back to the beginning of time.
THE BOHR ATOM
One of the most perplexing problems for earlytwentieth-century physicists was why the atom emits a discrete pattern of spectral lines. By 1913, when the structure of atoms was reasonably well known, Niels Bohr (1885-1962), a Danish physicist, proposed a theory for the structure of the simplest atom, hydrogen, whose one electron orbits around a proton. He suggested that the electron can occupy only a selected number of prescribed concentric orbits about the nucleus, rather than having an unlimited and unspecified orbital distance. Also, the electron normally resides in the lowest energy orbit, which is the one closest to the nucleus. Orbits representing higher levels of energy are increasingly farther from the nucleus. The diameter of the first orbit corresponds to the normal size of the hydrogen atom, about
10-8 centimeter in diameter.
When the atom absorbs energy, it is said to be excited, and the electron appears in one of the outer orbits, which have successively higher energies than the lowest orbit does. The electron's change (up or down) from one allowed orbit to another is called an electron transition. An atom in a gas may acquire the internal energy necessary to excite an electron by random thermal collisions with other gas atoms, collisions with subatomic particles such as free electrons, or absorption of a photon traveling through the gas.
Of all the photons striking the atom only those possessing an amount of energy equal to the energy difference between a higher energy orbit and the one in which the electron is located will be absorbed and excite the atom. For example, in the hydrogen atom it takes 10.2 electron volts, or 1.63 x 10-11 erg, of energy to raise the electron from its lowest energy orbit to the next higher energy orbit. Photons with energies below 10.2 electron volts will not be absorbed, and consequently the electron will not be excited. Photons with energies in excess of 10.2 electron volts cannot raise the electron to the second orbit, but they may, if they have the right amount of energy, excite the atom by lifting the electron to even higher energy orbits.
How long will an excited atom remain that way? If a gas atom is excited, then in about a hundredmillionth of a second it will rid itself of any energy in excess of that of the lowest energy orbit by emitting the energy in the form of one or more photons. Somewhat like a ball bouncing down a staircase, the electron will arop in succession into one or maybe several lower energy orbits on its way to the lowest energy level, where it can reside indefinitely. With each downward transition a photon of electromagnetic radiation is emitted. This photon represents the energy difference between the two orbits between which the electron makes the transition. The greater the energy difference, the greater is the amount of energy released in the form of a photon and, consequently, the shorter is the wavelength of the photon. Bohr was led to such a model for the atom as the most straightforward means of accounting for the discrete amounts of energy contained in photons. (Laboratory experiments had already shown that light really possessed the properties of a discrete phenomenon.)
Two examples from the countless electron transitions possible in the hydrogen atom are shown in Figure 4.14. Besides emitting energy spontaneously, an excited atom, before it can emit a photon, may collide with another atom in the gas and transfer energy to it as kinetic energy of motion. In this case no photon will be emitted.
SPECTRUM OF HYDROGEN ATOM
In addition to the model of the atom that represents it by its electron orbits, we can make a model using the energy of each allowed electron orbit. Such an energy-level model for hydrogen appears in Figure 4.16. The number of the energy levels corresponds in a one-to-one fashion with the number of the electron orbits. The distance between successive electron orbits increases with higher orbit numbers, but the differences in energy between successive orbits grows smaller as the orbit number increases.
Suppose a hydrogen atom is excited so that its electron is in the third energy level. Then it may de-excite directly to the ground state, emitting one photon. The photon would have a wavelength of 1026 angstroms,
which corresponds to the energy difference between these two orbits in the hydrogen atom. Or it may de-excite to the second energy level, emitting a photon with a wavelength of 6562 angstroms, and then de-excite from the second energy level to the ground state, emitting a photon with a wavelength of 1216 angstroms. The total energy emitted in both cases is the same, but the wavelengths that result and hence the spectral lines differ.
The hydrogen-line spectrum in the visible region, known as the Balmer series, is prominent in the absorption spectra of most stars. It arises from electron transitions originating on the second energy level of the atom. In the same way all the possible transitions from the ground level are known as the Lyman series, which is in the ultraviolet part of the electromagnetic spectrum. Those transitions from the third level up to higher energy levels are the Paschen series, which is in the infrared; and so on for the remaining series, whose lines appear in the far infrared on out to the microwave region of the spectrum.
Each series of spectral lines comes to a limit toward shorter wavelengths. The uppermost levels, representing the electron's highest energy orbits, crowd together toward a series limit, which represents the point beyond which the proton can no longer bind the electron to it. In this case the electron has been removed from the atom (it has been ionized) and is free to take on any energy.
If the electron is given enough energy, either by collision or absorption of a photon, it can escape the electrical attraction of the nucleus. The atom is then ionized and is in the form of a positive ion. The ionized hydrogen atom cannot absorb or reradiate energy in the form of discrete lines until it captures a free electron. It can execute the captu re because of the electrical force of attraction between the positively charged nucleus (the proton) and the negatively charged electron. Note that it converges toward its series limit at approximately 3646 angstroms.
SPECTRA OF OTHER ElEMENTS
In the Bohr atom, besides limits on the size of electron orbits, there is a limit to the number of electrons that may occupy a given orbit. These allowed orbits with a prescribed number of electrons in them are called electron shells.
In general, as one goes through the periodic table, electrons are added to balance the number of protons in the nucleus by filling the shells from the one closest to the nucleus outward. In hydrogen there is one electron in the innermost shell, which has room for a maximum of 2 electrons. Helium's 2 electrons fill, or close, the shell so that for the element lithium the third electron must start a new shell, which is the next innermost. In the second shell there is room for only 8 electrons; in the third, 18 electrons; in the fourth, 32; and so on.
Each element has a unique set of energy levels. Consequently, the wavelength of the spectral lines originating from electron transitions between various energy levels is also unique for each element-a clear fingerprint of the element.
The amount of energy needed to ionize an atom varies from one element to the next depending on the number and "position" of the electrons. For example, to remove the outermost electron from helium takes five times as much energy as it does to do the same for sodium. Also, for a given element each additional ionization takes more energy to free an electron from an inner orbit than from an outer one because the inner one is more tightly bound to the nucleus. Thus, with carbon as an example, it takes more than twice as much energy to remove the second electron than it does to remove the first; fou r times more for the third electron than the first; almost six times more for the fourth electron; thirty-five times more for the fifth electron; and a whopping forty-four times more for the innermost sixth electron than for the outermost first electron.
Multiple ionization of a carbon atom brings a corresponding readjustment of the energy levels because of the altered electrical attraction between the positive nucleus of the carbon atom and the reduced number of electrons. Altering the energy corresponding to each allowed orbit produces different spectral lines with each succeeding ionization of the carbon atom. So we see not only different wavelengths for absorption lines or emission lines between different unionized elements but for the same element a different spectrum after each ionization. That is, the spectrum of singly ionized carbon differs from the spectrum of neutral carbon; doubly ionized carbon differs from singly ionized; triply ionized differs from doubly ionized; and so on.
Using the properties of electromagnetic radiation, the atom's structure, the interaction between matter and energy, and spectrum analysis, astronomers have gained much information about the universe from the radiation it emits. And as we develop an even greater understanding of the nature of radiation-its formation, propagation, interaction with matter, and destruction-we can explore more deeply the dim sources in the outer reaches of the cosmos, almost back to the beginning of time.
