How Do You Know if Emissions Absorb or Emit Visible Light
Copyright © Michael Richmond. This piece of work is licensed under a Artistic Commons License. Emission and Assimilation Lines
Homework for tomorrow's course
People have long known that the stars are far, far away; in the nineteeth century, astronomers finally measured the distances to a few nearby stars with reasonable accurateness. The results were so big -- grand of trillions of miles -- that almost people figured we'd never be able to visit them or learn much near them. After all, nosotros can't go to a star, grab a sample, and bring it dorsum to world; all we tin practice is await at light from the star. In fact, at to the lowest degree 1 prominent philosopher and scientist went on the tape equally maxim that we'd never exist able to figure out their compositions.
Of all objects, the planets are those which appear to us under the least varied attribute. We see how nosotros may make up one's mind their forms, their distances, their majority, and their motions, but we can never known anything of their chemical or mineralogical structure; and, much less, that of organized beings living on their surface ...
- Auguste Comte, The Positive Philosophy, Volume II, Chapter 1 (1842)
(Comte refers to the planets in the quotation above; he believes that we tin learn fifty-fifty less about the stars)
Merely, information technology turns out, light from the star encodes a wealth of information most the physical country of its outer atmosphere. Light is produced in the inner regions of a star and works its manner out to the "surface" -- which is really a part of the gaseous atmosphere called the photosphere. Photons produced in the photosphere accept a adept chance to escape outwards into space and, somewhen, reach united states. Every bit photons fly through the outermost layers of the stellar atmosphere, however, they may be absorbed by atoms or ions in those outer layers. The assimilation lines produced by these outermost layers of the star tell u.s. a lot about the chemical compositition, temperature, and other features of the star.
Today, we'll look at the processes past which emission and absorption lines are created. We'll also practice a little flake of analysis, only leave most of it for a afterwards day...
Emission-line spectra
Depression-density clouds of gas floating in infinite will emit emission lines if they are excited by free energy from nearby stars. Planetary nebulae, for instance, are the remnants of stars which have gently pushed their outer envelopes outwards into space. Some of them are very pretty:
See Astronomy Picture of the Solar day for Oct 31, 1999
Meet Astronomy Picture of the Day for March 21, 1999
The hot cardinal stars which remain irradiate these wispy shells of gas with high-free energy ultraviolet photons, which excite the atoms in the gas and cause it to glow. The spectrum of a planetary nebula reveals almost nothing but very potent, narrow emission lines:
Retrieve that 10 Angstroms = 1 nm, then 4000 Angstroms = 400 nm = blue lite ...
What exactly did I mean by the phrase excite the atoms in the gas? And what does that have to exercise with these narrow emission lines? Let'southward take a look at the individual atoms in the gas around a planetary nebula....
Atomic energy levels and transitions
Individual atoms consist of a nucleus of positive charge surrounded past one or more than negative particles called electrons. To a crude approximation, the electrons circle the nucleus, somewhat as planets circle the Lord's day.
Q: What is the force which keeps planets in orbit effectually the Sun? Q: What is the forcefulness which keeps electrons in "orbit" around the nucleus? The answers
Unlike the orbits of planets and asteroids effectually the Sun, which may be any size, the orbits of electrons in atoms turn out to obey a rather peculiar set of rules.
- Only orbits of certain item radius are permitted
- Each orbit has a different potential energy: small orbits accept depression potential energy, big orbits accept high potential energy
- Electrons may spring between any two orbits, but do so instantaneously;
- for the electron to spring upwards, to a larger orbit, something must provide exactly the right amount of free energy to the atom
- for the electron to spring downwards, to a smaller orbit, the atom must get rid of exactly the right amount of energy
So, for case, one particular cantlet might have orbits with energy levels similar this:
In this example, the energy difference betwixt the 2d and beginning orbit is Δ E = six - 1 = 5 units. We'll hash out details of the units in a moment. Now, if a photon of 5 units of energy happens to see this atom, information technology might exist absorbed by the cantlet, exciting the electron from the beginning orbit to the second orbit.
Before ...
... and after.
Discover that the photon has disappeared.
One time y'all take excited an atom, all you have to do is expect a bit; somewhen, the atom volition bound back down to a lower energy state, emitting a photon itself.
The free energy of this emitted photon is exactly equal to the difference in atomic free energy levels between the initial and terminal states. In this case, the emitted photon would take 5 units of energy.
Because each type of atom has its own unique prepare of energy levels, each type of cantlet will emit light with a dissimilar set up of energies. And, given the human relationship between the energy Due east of a photon and its wavelength λ (or frequency ν)
that means that each type of atom volition produce a fix of emission lines at its own unique wavelengths.
Oh, by the way, in case you lot aren't familiar with these symbols, here are their definitions. We'll see a more than convenient grade of the equation above in only a few minutes .... Planck constant h = half dozen.636 x ten^(-34) Joule-sec speed of light c = 2.998 x 10^(8) meter/sec Example: the spectrum of hydrogen
For example, consider hydrogen, the simplest (and most mutual) element in the universe. It consists of a single proton in its nucleus, around which a single electron orbits.
The energy levels of a hydrogen atom follow a regular pattern. The free energy of level due north is given by a unproblematic formula:
Sometimes it helps to make a picture of the energy levels.
We put the "ground state" level, north=one, at the bottom of the diagram. At the meridian, we put the level at which the cantlet will exist ionized: if information technology gains this much energy, the electron flies off into space, never to return.
We tin can depict an atomic transition graphically by drawing a trivial ball on the diagram to represent the energy of the atom. If the atom drops from a high level to a lower i, information technology will emit a photon. The energy of the photon is equal to the deviation between the initial and concluding free energy levels.
Q: What is the energy of the photon emitted when a hydrogen atoms drops from north=2 to n=ane? The answer
As mentioned earlier, the energy of a photon determines its wavelength. You can catechumen from one to the other via a formula
where h is Planck'south abiding and c is the speed of low-cal. The combination h times c has the convenient value of 1240 eV*nm, so
Q: What is the wavelength of the photon emitted when a hydrogen atoms drops from due north=2 to northward=one? Could y'all see that photon with your eye? The answer
Q: What is the wavelength of the photon emitted when a hydrogen atoms drops from n=three to n=2? Could you see this photon? The answer
Transisions in which a hydrogen atoms drops down in energy to the second level are called Balmer transitions, after the scientist who first measured their properties very advisedly. Since they occur in the visible portion of the spectrum, and they involve the well-nigh common element in the universe, they are one of an astronomer'southward most powerful tools. If yous look again at the spectrum of the planetary nebula, you'll see several Balmer lines:
Call up that 10 Angstroms = 1 nm, so 4000 Angstroms = 400 nm = blue lite ...
Other atoms take spectra which are more complex than that of hydrogen; there are no simple formulae describing their energy levels. Fortunately, many scientists accept spent years measuring the wavelengths of low-cal emitted and absorbed past almost every variety of cantlet (and ion, and molecule) you can imagine. Y'all can await up the wavelengths for whatsoever detail material in one of several big compilations of spectral lines.
- Line Spectra of the Elements, by J. Reader and Ch.H. Corliss
- Atomic spectral line list, past R. Hirata and T. Horaguchi
- A revised version of the Identification List of Lines in Stellar Spectra (ILLSS) Catalogue past R. Coluzzi
Absorption lines
A loftier-resolution spectrum of the Lord's day shows many, many, MANY dark absorption lines:
Absorption lines are based on the same concrete principle equally emission lines: they involve an atom jumping from one item energy level to another. In this case, nonetheless, the jumps must be upwards, from a low level to a higher one.
For example, if a photon of wavelength 121 nm happens to fly past a hydrogen atom in its ground land,
the hydrogen atom will absorb the photon and hop up to the n=two level.
That means that if we look at a source of continuous radiations
through a cloud of hydrogen gas, we will see a dark absorption line at 121 nm.
We run into absorption lines in the spectra of ordinary stars similar the Sun because the tenuous outer layers of the stellar temper -- called the photosphere -- blot some of the continuous light coming from the hot, dense interior.
The conditions needed to produce line spectra
Emission and absorption lines tin tell us a bang-up bargain nigh a afar celestial source, but they only occur under certain conditions.
Emission lines from an element will appear if
- in that location are atoms of the chemical element present
- the atoms are in a low-density gas
- the atoms are excited into a particular high energy level past some external source
Absorption lines from an chemical element will announced if
- there are atoms of the element nowadays
- the atoms are in a low-density gas
- the atoms spend most of their time in a particular low-energy level
- the gas lies between us and a source of contiunous light (of all wavelengths)
Below are a set of spectra of three different real stars and one theoretical, simulated star. All three stars have like temperatures in their photospheres, so the differences in the assimilation lines of any one detail element practice indicate differences in the affluence of that chemical element.
Image courtesy of the European Southern Observatory
On the other hand, if you're not careful, spectral analysis might lead y'all astray. Let'southward compare the spectra of our ain Sun with that of the brilliant star Vega.
Image courtesy of Michael Lemke and Simon Jeffrey
Hither are the spectra shown as a graph, rather than as a picture. You can see the Balmer assimilation lines of hydrogen in the spectrum of Vega very clearly.
Q: What element makes up most of the star Vega? Q: What element makes up most of the Sunday? Q: Why don't the absorption lines of hydrogen dominate the spectrum of the Sun, too? The answer isn't obvious. In the early 1900s, astronomers didn't understand information technology, and they idea that Iron was 1 of the most common elements in the Sun'south atmosphere, while hydrogen was a pocket-sized constituent. The person who solved this puzzle and figured out the true composition of the stars was a young woman named Cecilia Payne.
Homework for tomorrow'due south grade
- Print a copy of the spectrum of the planetary nebula PN G000.2+06.1, which is shown at the meridian of this lecture. On the printed copy,
- place and mark the emission lines which are due to Balmer transitions of hydrogen atoms; you should be able to find at least 3 or four
- for each of these lines, write down the initial energy level and the concluding energy level involved in the transition (i.eastward. for the line at 656 nm, you would write "initial n=3, final n=ii")
- Expect at the stellar spectrum below.
- Estimate the temperature of this star.
- Sodium atoms have the following free energy levels: (sort of -- I've assigned some new numbers)
n free energy (eV) ------------------------- ane -5.14 two -three.04 three -ane.96 4 -1.52 -------------------------Ane of the strongest lines in the spectrum above is due to a transition in sodium atoms. Which one is it? What is the wavelength, and what are the levels involved?
For more data
- Looking for the source of some particular spectral line? Check out the Spectra of Gas Discharge page.
- Y'all might also play with the MiniSpectroscopy Java Applet
- The spectra of planetary nebula shown above come from a paper past Mantiega et al., AJ 127, 3437 (2004)
How Do You Know if Emissions Absorb or Emit Visible Light
Source: http://spiff.rit.edu/classes/phys301/lectures/spec_lines/spec_lines.html
0 Response to "How Do You Know if Emissions Absorb or Emit Visible Light"
Post a Comment