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General Astronomy Spectra. Spectra. Early in this course, it was noted that we only detect light from the stars. They are too far away to do much more than that. As such, we can see: Brightness Position Color. Color.
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Spectra Early in this course, it was noted that we only detect light from the stars. They are too far away to do much more than that. As such, we can see: • Brightness • Position • Color
Color Recall that we can separate the star's visible light into its component colors by use of a prism
Color We can also use a Diffraction Grating to disperse light into its component colors. A grating is thousands of 'slits'
The Continuous Spectrum Kirschoff's First Law: A hot solid, liquid or dense gas produces a continuous spectrum
The Continuous Spectrum Solid
The Continuous Spectrum GAS Compact Fluorescent Bulb Note the gaps in the spectrum
The Continuous Spectrum and Temperature • Blackbody Radiation • A blackbody (a perfect absorber and emitter of radiation) relates its color to its temperature
The Continuous Spectrum and Temperature Wein's Law relates the wavelength of greatest intensity to the temperature λmax = 2.88x107 / T Where wavelength is in Angstroms and temperature is in Kelvin For example, the surface temperature of the Sun is about 5980K. So, 2.88x107 / 5980 = 4816 angstroms, (a yellowish color)
The Continuous Spectrum and Temperature Stefan-Boltzmann Law relates the total amount of energy radiated to the temperature of the body: E = σ T4 For example, the Sun’s surface temperature is about 6000K; Your skin temperature is about 300K. The Sun’s surface is about 20 times hotter than your skin. But what’s the difference in energy radiated? Esun / Eskin = σ Tsun4 / σ Tskin4 =(Tsun /Tskin)4 = (20)4 = 160,000
Blackbody in Infrared Much of a person's energy is radiated away in the form of infrared energy. Some materials are transparent to infrared light, while opaque to visible light (note the plastic bag). Other materials are transparent to visible light, while opaque or reflective to the infrared (note the man's glasses).
The Emission Spectrum Kirschoff's Second Law: A hot, rarified gas produces an emission, or bright line, spectrum
The Absorption Spectrum Kirschoff's Third Law: A cool, rarified gas produces an absorption, or dark line, spectrum
ComparingThe Bright and Dark Lines Notice that, for a given element, the bright and dark lines in the spectrum show up in exactly the same positions (actually this depends on the temperature of the gas – but we'll discuss this later)
Bohr Theory What’s wrong with the Rutherford model of the atom? • Let’s put together some facts: • By Newton’s 1st Law, an electron circling a nucleus must be accelerating • An accelerating charge radiates • Charges that radiate, lose energy • Loss of energy + conservation of angular momentum mean that the electron must spiral into the nucleus. The charges annihilate each other and destroy the atom Doesn’t seem to happen, Does it?
Bohr Theory • Niels Bohr came up with a radical idea • If the electron stays within certain allowed orbits, it will not radiate. • These allowed orbits are called ‘energy levels’ • An electron may move between energy levels by absorbing or emitting the exact difference in energy between the levels While Bohr Theory is not “correct” it provides an easy model – which is adequate to explain the spectra we will observe.
n = 3 n = 2 1st Excited State, n = 1 Ground State, n = 0 Bohr Theory: The H atom The first few energy levels
Brackett 13.6 13.0 Paschen 3 12.7 Balmer 2 12.0 1 10.2 Lyman 0 Hydrogen Spectral Series The Balmer Series of lines are in Visible Light
External Influences The Zeeman Effect
External Influences The Stark Effect Like a magnetic field, an Electric field can also cause a spectral line to split into components. The difference is this type of splitting is not symmetrical (like the magnetic type). This is known as the Stark Effect
A Spectral Line Let's magnify a single spectral line. Normally we would be looking at absorption lines, but it is easier to see an emission line on the slides. Funny, you would think that an exact amount of energy would produce a very thin line. What is causing the 'spread' in the shape of the line?
The Heisenberg Uncertainty Principle Early last century, Werner Heisenberg stated a guiding principle, known as the Uncertainty Principle. It can be stated in two possible, but equivalent, ways: 1. The better you can fix the location of an object, the worse you can fix its momentum and vice versa. 2. The better you can fix the energy of an object, the worse you can fix its time duration and vice versa.
Natural Line Widths The photons emitted by an atom are related to the amount of energy given up by a electron moving between the levels. Since the time that an electron stays in a level varies by a tiny amount, then – via Heisenberg – the small difference in time causes a small difference in energy and therefore a small spread in wavelength
Doppler Broadening This extra spreading of a spectral line is caused by the Doppler Effect – sources of light moving toward us ('blueing' the light) and away from us ('reddening' the light. This generally occurs through three mechanisms: • Turbulence • Motions of masses of gas churning in the star • Pulsing • The surface of the star expanding and contracting • Rotation • Rapid rotation of the star
Pressure Broadening Sometimes called Collisional Broadening, as the atoms are squeezed together by gas pressure in the star, they are more likely to collide. Collisions may cause the photon to be created with (again the Uncertainty Principle) slightly different energies. Also, as the atoms become closer together their electric fields start to cause the Stark Effect causing a slight splitting of the line which also looks like broadening when unresolved.
