Tuesday, January 23, 2018

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Chemistry - Spectroscopy

Much of our knowledge about atomic structure comes from experimental data relating the interaction between light and atoms of the different elements. Light may be modeled as an electromagnetic wave, consisting of an oscillating electric field and an oscillating magnetic field. Like any wave, the relationship between propagation velocity, wavelength, and frequency is described by the following equation:

v = λf

Where,

v = Velocity of propagation (e.g. meters per second)

λ = Wavelength (e.g. meters)

f = Frequency of wave (e.g. Hz, or 1/seconds)

 

When applied to light waves, this equation is typically written as c = λf, where c is the velocity of light in a vacuum: one of the fundamental constants of physics.

Light that is visible to the human eye has wavelengths approximately between 400 nm (400 nanometers) at the violet end of the spectrum and 700 nm at the red end of the spectrum. Given the velocity of light (approximately 3 × 108 m/s), this equates to a frequency range for visible light between 7.5 × 1014 Hz and 4.286 × 1014 Hz.

A computer-generated image of the visible light spectrum (plus the ultraviolet and infrared regions outside of the visible range, shown in grey) appears here. A real spectrum may be generated by taking “white” light and passing it through either a prism or a diffraction grating so that the different wavelengths separate from each other:

 

Just like buoyant objects are moved up and down by waves of water, electrically-charged objects may be moved about by waves of electrical fields such as light. In the case of electrons, their positions around the nucleus of an atom may be altered if struck by light of the correct wavelength.

One of the major breakthrough discoveries of modern physics was the realization that a ray of light could be modeled as a particle (called a photon) possessing a definite amount of energy, in addition to being modeled as a wave with a definite frequency. The combined work of physicists Max Planck in 1900 and Albert Einstein in 1905 resulted in the following equation relating a photon’s energy to its frequency:

E = hf

Where,

E = Energy carried by a single “photon” of light (joules)

h = Planck’s constant (6.626 × 10-34 joule-seconds)

f = Frequency of light wave (Hz, or 1/seconds)

 

We may re-write this equation to express a photon’s energy in terms of its wavelength (λ) rather than its frequency (f), knowing the equation relating those two variables for waves of light (c = λf):

 

If the amount of energy carried by a photon happens to match the energy required to make an atomic electron “jump” from one energy level to another within the atom, the photon will be consumed in the work of that task when it strikes the atom. Conversely, when that “excited” electron returns to its original (lower) energy level in the atom, it releases a photon of the same frequency as the original photon that excited the electron.

Since the energy levels available for an electron to “jump” within an atom are limited to certain fixed values, this means only certain specific frequencies or wavelengths of light will be able to make an electron of a particular atom move to new shells and/or subshells. The sentence you just read is actually backward from an historical perspective: what came first was the discovery that only certain wavelengths of light were associated with atomic energy changes, and from that came the extrapolation that the energy levels of atomic electrons must be quantized (limited to definite, fixed values and not continuously variable as previously thought). This was a tremendous discovery, and it put physics on a whole new path toward a quantum model of matter and energy.

This is why the notation used in the previous section to describe electron configurations (e.g. 1s22s22p1) is called spectroscopic notation: the discovery of shells, subshells, and orbitals owes itself to the analysis of light wavelengths associated with different types of atoms, studied with a device called a spectroscope constructed to analyze the wavelengths of light across the visible spectrum.

 

Emission Spectroscopy

If we take a sample of atoms, all of the same element and at a low density1 (e.g. a gas or vapor), and “excite” them with a source of energy such as an electric arc, we will notice those atoms emit colors of light that are characteristically unique to that element. The unique electron configurations of each element creates a unique set of energy values between which atomic electrons of that element may “jump.” Since no two elements have the exact same electron configurations, no two elements will have the same exact set of available energy levels for their electrons. When excited electrons fall back into their normal (“ground state”) energy levels, the photons they emit will have distinct wavelengths. The result is an emission spectrum of light wavelengths, much like a “fingerprint” unique to that element. Indeed, just as fingerprints may be used to identify a person, the spectrum of light emitted by an “excited” sample of an element may be used to identify that element!

For example, we see here the emission spectrum for hydrogen, shown immediately below the continuous spectrum of visible light for convenient reference2:


Each of the colored “lines” in the emission spectrum for hydrogen represents the photon wavelength emitted when the excited electron loses energy and falls back into a lower-level position. The larger the energy difference between energy levels (i.e. the bigger the jump), the more energy the photon carries away, and consequently the shorter the wavelength (higher the frequency) of the photon. The violet color line, therefore, represents one of the larger “jumps” while the red color line represents one of the smaller. Hydrogen happens to emit four different wavelengths within the visible range (656 nm, 486 nm, 434 nm, and 410 nm)3, and many others outside the visible range.

This next graphic shows the emission spectra of several elements contrasted against a continuous spectrum covering both visible light and portions of the ultraviolet and infrared ranges:

Note how complex the emission spectra are for some of the elements, and how spectral lines for most elements (including hydrogen) extend past the visible light range.

Not only may the wavelengths of photons emitted from “excited” electrons returning to lower energy conditions be used to positively identify different elements, but we may also use those wavelengths as universal standards, since the fundamental properties of elements are not liable to change. For example, the SI (Syst`eme International) definition for the base unit of the meter is standardized as 1,650,763.73 wavelengths of light emitted by a krypton-86 (86Kr) atom as its electrons transition between the 2p10 and 5d5 subshells4.

 

Absorption spectroscopy

If we take a sample of atoms, all of the same element and at a low density (e.g. a gas or vapor), and pass a continuous (“white”) spectrum of light wavelengths through that sample, we will notice certain colors of light missing from the light exiting the sample. Not only are these missing wavelengths characteristically unique to that element, but they are the exact same wavelengths of light found in the emission spectrum for that element! The same photon wavelengths produced by an atom when “excited” by an external energy source will be readily absorbed by that atom if exposed to it. Thus, the spectrum of light missing characteristic wavelengths after passing through a gas sample is called an absorption spectrum, and may be used to identify elements just as easily5 as an emission spectrum.

The absorption spectrum of hydrogen gas is shown at the bottom of this three-spectrum graphic image, contrasted against the continuous spectrum of visible light (top) and the emission spectrum for hydrogen (middle):

Note how the four colored lines in the emission spectrum characteristic of hydrogen appear as missing colors (black lines) in the absorption spectrum. It is almost as though one spectrum were a photographic “negative” of the other: each of the colors present in the emission spectrum is distinctly missing in the absorption spectrum. Although the color patterns may be inverted, the positions of the lines within the spectrum are the same, and are uniquely representative of hydrogen. Individual atoms are not the only forms of matter possessing uniquely identifying spectra – many molecules have spectral “signatures” of their own as well. The absorption spectra for molecular substances are substantially more complex than the absorption spectra of pure elements, owing to the many more different ways in which light energy may be absorbed by a molecule. In addition to electron shell and subshell “jumps” capable of absorbing a photon’s energy, the atoms within a molecule are also able to vibrate, rotate, and twist about each other like mechanical oscillators. Photons of light possessing just the right frequencies are able to “excite” certain molecules in a manner not unlike AC electrical waveforms resonating with tuned LC (inductor-capacitor) circuits. Just as tuned LC circuits absorb and store energy at certain frequencies, molecular oscillators absorb and store energy from photons.

The multiplicity of energy-absorbing modes for certain molecules gives them wide bands of absorption in the light spectrum, not just thin “lines” as is the case with individual atoms. These bands are still unique to each molecule type, but they typically cover a far broader swath of wavelengths than is typical for atomic absorption spectra.

The absorption of ultraviolet light by ozone gas (O3) high in Earth’s atmosphere is an example of absorption spectroscopy on a grand scale. These molecules serve as a protective “blanket” against ultraviolet light rays from the sun which have detrimental effects on life (e.g. sunburn, skin cancer). The ozone does not absorb light in the visible spectrum, and so its protective effects are not visually apparent, but the attenuation of ultraviolet light is definitely measurable. This attenuation also covers far more than just one or two specific wavelengths of ultraviolet light, which is good for life on Earth because otherwise ozone wouldn’t offer much protection.

Many chemical substances of interest in process industries have well-known absorption signatures for ultraviolet and infrared light. This makes spectroscopy a powerful tool for the identification (and quantitative measurement) of chemical composition in process fluids, exhaust gases, and sometimes even in solid materials. 

 

1Solids and liquids tend to emit a broad spectrum of wavelengths when heated, in stark contrast to the distinct “lines” of color emitted by isolated atoms.

2To create these spectra, I used a computer program called Spectrum Explorer, or SPEX.

3These wavelengths are part of the Balmer series of spectral lines, corresponding to electrons falling from the 3rd, 4th, 5th, and 6th shells down to the 2nd shell. Photons emitted by excited electrons returning to the “ground level” shell lie outside the visible range, since the transition from the second shell (L shell, n = 2) to the first shell (K shell, n = 1) is a much larger energy gap, producing a photon of much greater energy and shorter wavelength (approximately 122 nm) than those found within the visible light spectrum.

4The wavelength of this light happens to lie within the visible range, at approximately 606 nm.

5In fact, it is often easier to obtain an absorption spectrum of a sample than to create an emission spectrum, due to the relative simplicity of the absorption spectrometer test fixture. We don’t have to energize a sample to incandescence to obtain an absorption spectrum – all we must do is pass white light through enough of it to absorb the charcteristic colors.

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