Chapter 3

Atoms– tiny wonders worth studying

Dalton's original atomic theory had faults, but the basic idea that materials consist of tiny natural units is fundamentally correct and sound. To his credit, these natural units are widely accepted as atoms, whose shape is not known. However, we generally assume them spherical. Evidences show their radii being in the order of 10-10 m. For convenience, such a length is called an Angstrom, (symbol Å). The unit nanometer (10–9 m, symbol nm) is used more often in modern literature. The atomic radii are in the order of tenth of nanometers. For example, the atomic radii of potassium, iron and copper are 0.235, 0.116 and 0.117 nm respectively. Look at them another way. Some hundred millions of atoms line up to give a length of just one cm. Atoms are very tiny indeed, but they are wonders to study.

Three quarks for muster Mark, sure he hasn't got much of a bark

J. Joyce

in Finnegan's Mark1

As a comparison, the wavelength of visible light ranges from 350 (red) to 700 (violet) nm, thousand times larger than the atomic radii of atoms. Using visible light to see atoms is impossible.

Studying the invisible tiny atoms is a challenge. Fortunately, driven by energy, these tiny wonders undergo changes. The study of energy absorbed and emitted in the form of electromagnetic radiation is called spectroscopy. Spectroscopic results revealed information about the tiny wonders.

Since Newtonian physics cannot explain phenomena of individual atoms a new theory called quantum mechanics is required for their explanation. The formulation of this new theory generated new concepts. Thus, the study of these tiny wonders is rewarding because we acquire new tools to understand and interpret atomic phenomena.

As we study the tiny wonders, new phenomena such as X-rays and radioactivity were discovered. These discoveries in turn are tools for the study of atoms as well as for other applications. Using one of these tools, Rutherford revealed the structure of atoms. The atoms consist of electrons and a very small heavy core called atomic nucleus. Almost all the atomic mass is concentrated on the nucleus. The space occupied by an atom is mostly due to electrons.

Atomic Spectroscopy

In general, the study of electromagnetic radiation is called spectroscopy. It is one of the oldest branches of science, yet it is continually evolving as new techniques are developed. Results from spectroscopic studies reveal not only secret of nature, its techniques have many applications. Electromagnetic radiation is emitted from atoms, and atoms also absorb this form of energy. The study of radiation emitted or absorbed from tiny atoms is called atomic spectroscopy, which involves light in the regions of infrared, visible, ultraviolet, and X-ray.

Visible Light

A narrow band of electromagnetic radiation that stimulates the sensory centers of our eyes is called visible light. Our eyes are excellent detectors for them. Therefore, ancient people knew something about visible light. They saw a beam of white light dispersed into colored beams through a prism. Newton also studied visible light. He combined the colored light beams from one prism into a white beam by using a second prism.

The color of a light beam dispersed from the prism depends on its wavelength or the associated frequency. The wavelength increases whereas the frequency decreases from violet to red light.

You have learned that a light beam consists of photons. The intensity of a beam is proportional to the number of photons. The distribution of intensity versus frequency (or wavelength) is a spectrum.

A white light consists of photons with all frequencies in the visible region, and it has a continuous spectrum, with intensities varying continuously as a function of the frequency. An object with various amounts of energies for light emission, such as a hot solid, emits a white light beam.

A combination of red, green and blue light beams also gives us a sense of a whit light, but such a light consists of only three lines when dispersed by a prism. Such as spectrum, when plotted, consists of three peaks. Such a spectrum is an example of a line spectrum, which in general consists of some lines when dispersed by a prism. A hot gas, such as the flame of a fire emits a light beam with a lime spectrum. A real hot gas consists of individual atoms. These atoms have certain extra amounts of energy and they release them in the form of radiation. Thus, if we want to study the atomic spectrum of an element, we usually study the light from a hot gas of the element. For example, when a salt solution is introduced into a hot flame, you will see the characteristic yellow sodium D line.

A gas absorbs light of certain frequencies. Thus only some of the photons of a white light beam will be absorbed when it passes through a gas. The spectrum will have some dark lines due to the absorption. Such a distribution of intensity is called an absorption spectrum, or dark-line spectrum.

Spectroscopy studies radiation in the entire electromagnetic spectrum. Continuous, line and absorption spectra are not limited to those appear in the visible region. They also apply to microwave, infrared, ultraviolet, X-ray and gamma ray regions.

Skill Building Questions:

  1. What is light? (see Electromagnetic Radiation in the Chapter on Energy)
  1. What is a spectrum? What are continuous, line and absorption spectra?
  1. What is white light? How can it be separated into its components according to frequencies or wavelengths?

Line Spectra of Atoms

As mentioned earlier, light emitted by a hot gas has a line spectrum. When a white light beam passes through a gas, a dark-line spectrum is observed.

  • What is the significance of line spectra?
    What applications can be made of the atomic spectra?

In order to study the emission spectra, R.W. Bunsen (1811-1899) and G.R. Kirchhoff (1824-1887) dispersed the light from a Bunsen burner. They observed the spectrum using a telescope mounted on a rotating table. They recognized that each element, when burned in a Bunsen burner, emit a unique spectrum. For example, all compounds containing sodium, Na, burned in a burner give a bright yellow color. Compounds containing copper give a blue or green color depending on the temperature.

Mercury lamps were used for road illuminations because they were bright. However, they cause a glare to the eyes. Especially on highways, the glare causes temporary blindness to drivers, creating dangerous situations. The yellow light from sodium lamps is soothing to the eyes and causes no glare. Thus, more sodium lamps are used to illuminate the highways now. Sodium light bulbs contain sodium vapor.

W.H. Wollaston (1766-1828) first observed some black lines appearing in the continuous spectrum of sunlight. For example, when a bean of white light passes through a gas containing sodium atoms, the yellow light is absorbed. A dark line appears in the yellow region.

Gas of an element not only emits a unique line spectrum, it also gives rise to a unique absorption spectrum. This was known during the early stages of science development. Thus, spectra serve as fingerprints of elements, and they have been used to confirm the presence or absence of a certain element in a sample. Thus, atomic emission spectroscopy and atomic absorption spectroscopy have been used for chemical analysis.

During the search for chemical elements in the 18th century, there was no method for the confirmation of a substance as an element. When a substance was first thought to be a chemical element, there was no guarantee that it would not someday be decomposed into simpler substances. Spectroscopy was intensely studied and the results are used for elemental confirmation.

Skill Building Questions:

  1. How can spectroscopy help to confirm a substance as a chemical element?
  1. What is the color of the flame when sodium ion is introduced to it? Why are sodium lamps used for highway illumination? What advantages do they have over other lamps? (Get information from other source).

Line Spectra of Hydrogen

The visible spectra can easily be studied using the spectrometer invented by Bunsen and Kirchhoff. The hydrogen spectrum has been intensely studied, and it consists of these lines: red, (wavelength 656.3 nm), green (486.1 nm), blue (443.0 nm), indigo (410.1 nm), and violet (396.9 nm). Early spectroscopists asked these questions.

  • Is there any regularity among these lines?
    What is the rule governing the regularity?

In 1885, a Swiss schoolmaster Johann J. Balmer (1825-1898) published a paper giving an empirical relationship for the wavelength  of the prominent lines of the hydrogen spectrum as:

nm(Balmer series)

0

where n is a whole number, (n = 3 for the red, 4 for the green, 5 for the blue, 6 for the indigo, and 7 for the violet lines). Johannes R. Rydberg (1854-1919) of the University of Lund revised the Balmer formula by taking the reciprocals of both sides. The reciprocal of wavelength (1/) is the number of waves per unit length, and it is referred to as the wave number (). The revised formula is now commonly expressed as:
 =(Revised Balmer series)
0

where R is the Rydberg constant (= 10973731.534 m-1), and n the same whole number given by Balmer. In words, a plot of  against 1/n2 is a straight line.

At that time, other spectroscopists tempted to speculate that a series of lines represented by the next formula existed,
 =(Lyman series)
0

Indeed, such a series of lines had been detected and confirmed by Lyman, and these lines are known as the Lyman series, whereas the series discovered by Balmer is called the Balmer series. The wave numbers of the lines in the Lyman series are higher, their average photon energy 4 times higher than that of the Balmer series. The Layman series was found in the ultraviolet region of the electromagnetic spectrum. Paschen found a low frequency series in the infrared region that satisfy this formula:

 =(Paschen series)

Recall Max Planck’s assumption that photon energy is proportional to the frequency or the wave number (see the Chapter on Energy),
E = h  = h c 
where h is the Planck constant and c the velocity of light.

Planck's theory of light emission led to the development of a theory called quantum mechanics, which suggests that the electron in an hydrogen atom can be at some definite energy levels. The energy of a level, En, can be represented by En,= – R, where n is a whole number. Note that a negative sign is given here so that it agrees with the original formula. An electron with En,= 0 corresponds to the energy of a free electron (not associated with any atom). A free electron can acquire any kinetic energy, and the energy states (or levels) above En,= 0 form a continuous band. Once the electron is trapped by a hydrogen nucleus, the electron can only be at an allowable energy state, En, with n being an integer. When n = 1, E1 has the lowest possible value, and this state is called the ground state. An energy diagram is shown here for such a system. Energy levels for n = 1, 2, 3, … are represented by long horizontal lines.

For a hydrogen atom, the energy made available for emitting a photon from energy level n to ni are thus given by
En-Eni=–R.
The arrows in the diagram indicate these transitions from one energy-level to a lower energy-level. The transitions corresponding to ni = 1, 2, and 3 are the Lyman, Balmer and Paschen series respectively.

ni = 1 for Lyman series,
;2 for Balmer series,
3 for Paschen series

Since n can be any integer greater than ni, many more series are expected if nature really follows this regular pattern. However, other series than the three mentioned above have very long wavelengths and they are unlikely observable. The three series mentioned here is sufficient to make the point.

Review Questions:

  1. Express the Rydberg constant R in terms of the value (364.56) given by Balmer.
  1. Calculate the four highest wave numbers for the four lines in each of the Layman series, the Balmer series, and the Paschen series. Give the energies of the lines in eV units.
  1. What is the mass equivalence in amu of the most energetic photon of the hydrogen spectrum?
  1. Use the energy-level diagram to explain the absorption spectrum of hydrogen.

The Discovery of X-rays

During the period when J.J. Thomson experimented with cathode rays, so did many other scholars, including W.C. Röntgen[*]. In one late afternoon, he walked between the cathode-ray tube and a fluorescence screen. Unexpectedly, he saw a shadow of his skeleton on the screen. He became so excited that he forgot to go home (upstairs in the same building) for dinner. His wife eventually came to see what was the matter with him. When she arrived, he showed her the mysterious rays he just discovered. He asked her to put her hand on top of a wrapped photographic plate, which was placed near the cathode ray tube. After the cathode-ray tube was turned on for a while, his plate recorded an image of her hand bones plus the ring on her finger. He sent a letter and the photograph to the magazine Nature. His letter published in Nature (Jan. 23, 1896) proclaimed his discovery of X- rays. He did not know what X-rays were.

2The X-ray photograph published by Röntgen (Nature, Jan. 23, 1896) showing a ring on the 3rd finger.

  • What are the X-rays and how to study them?
    What are their properties and applications?
  • Why and how are X-rays generated?
    Can they be generated by other methods?

Despite his ignorance of the nature of X-rays, Röntgen observed that X-rays penetrate paper, wood, aluminum and flesh. He is the first Nobel Prize winner (1901) in physics for this discovery.

Over the years, many argued that if Röntgen did not proclaim his discovery someone else would have, because X-rays are generated whenever cathode rays are in operation. During the operation, when high-energy electrons (cathode rays) striking a metallic or fluorescence plate, X- rays are generated.

In today’s technologies, X-rays are generated on TV tubes and computer monitors tubes. Electrons are accelerated to some thousand volts before they strike the fluorescence screens. Stopping the electrons by the screen produces fluorescence and generates X-rays. Bright and dark spots due to intensity of fluorescence form the images for us to see, but the X-rays generated are hazardous. However, these tubes are engineered to reduce the X-ray emission to save levels.

Eventually, we have learned that X-rays are electromagnetic radiation as light is. They form part of the electromagnetic radiation spectrum, with wavelengths in the order of 1 to 0.01 nm, compared to 350 to 700 nm in the visible region. Energies of these photons are in the range of 120–12000 eV compared to1-3 eV for photons in the visible region. Due to their very short wavelengths or high-energies, properties of X-rays are very different from those of visible light.

The spectrum of X-rays generated depends on the target material and on the energy of the electrons. For example, when the accelerating voltage is low, the X-rays have a continuous spectrum with a range of wavelengths, as we shall see shortly in the next paragraph.

A spectrum of X-rays, is usually a plot the number of photons (or intensity) against their energies. Sketches of two such spectra are shown here, one corresponding to low voltage electrons and one to high-energy electrons. There is a shift of energy as well as intensity when the voltage varies. The intensities increase and the peak with the highest intensity shifts to higher energy. The emission of X-rays is similar to the emission of white radiation by a hot solid. Both produce continuous spectra. X-rays are high-energy ionizing photons. X-ray intensities are measured by the same technologies as those used to measure radioactivity or ionizing radiation, and their discussion will be given later in a chapter after you have learned more about radioactivity.

Review Questions:

  1. How are X-rays generated? What are white X-rays and characteristic X-rays?
  1. Calculate the wave number and the frequency of the characteristic X-rays of copper. (1.17x1011 m–1 and 1.95x1018 Hz)

Properties of X-rays and Crystals

Although many properties of X-rays such as their ability to penetrate flesh, wood, black paper etc. have been measured, the real nature of X-ray was not clear. Here are some fundamental questions to start with.

  • What are X-rays, particles or waves?
    What experiment will show X-rays as particles and what experiment will show X-rays as waves?
  • If X-rays are particles, what are their masses?
    If X-rays are waves, what are their wavelengths, and how to measure them?

In many aspects, X-rays behave like particles. They penetrate wood, paper, aluminum, and soft tissues, propagating in a straight line when unhindered. X-rays are invisible to the naked eyes, but X-rays cause fluorescence on materials such as zinc sulfide. The material absorbs the energy of the X-rays and gives out fluorescence, which is visible.

As mentioned in Chapter 1, Newton rings observed on soap bubbles or thin oil films have been explained as due to interference of light as waves. Interference of waves is a phenomenon due to their diffraction, which is used to test wave properties.

A diffraction grating consists of a regular two- or three-dimensional array of objects or openings that scatter light according to its wavelength. The distance must be comparable with the wavelength of the light. In 1912, von Laue[*] reasoned that distances between atoms in crystals would be similar to the wavelength of X-rays. Consequently, his students Friedrich and Knipping subjected a crystal of zinc sulfide, ZnS, to a beam of X-rays and took a photograph of the beam. The image consisted of several poorly resolved spots, indicating that diffraction had occurred. The experiment showed that X-rays are indeed waves. Laue's reasoning was excellent, and he was awarded the Nobel Prize for physics in 1914.