General AstronomySpectra

SpectraEarly 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

ColorRecall that we can separate the

star's visible light into its component colors by use of a prism

ColorWe 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

Solid

The Continuous Spectrum

GASCompact Fluorescent Bulb

Note the gaps in the spectrum

The Continuous 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

For example, the surface temperature of the Sun is about 5980K. So,

2.88x107 / 5980 = 4816 angstroms, (a yellowish color)

Where wavelength is in Angstroms and temperature is in Kelvin

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 Tskin

4 = (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

Kirschoff's Laws

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 TheoryWhat’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.

Bohr Theory: The H atomThe first few energy levels

Ground State, n = 0

1st Excited State, n = 1

n = 2n = 3

Hydrogen Spectral Series

10.2

12.0

12.7

13.0

13.6

0

1

2

3

Lyman

Balmer

Paschen

Brackett

The Balmer Series of lines are in Visible Light

External InfluencesThe Zeeman Effect

External InfluencesThe 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 BroadeningThis 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:1. TurbulenceMotions of masses of gas churning in the star

2. PulsingThe surface of the star expanding and contracting

3. RotationRapid rotation of the star

Pressure BroadeningSometimes 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.