Chapter 3: Spectral lines in stars. Emission and absorption of light Emission line spectrum...

Chapter 3: Spectral lines in stars

Emission and absorption of light

Emission line spectrumContinuous spectrum(thermal, blackbody)

Independent of composition

Dependent on composition

Each element has its own unique spectrum

Absorption lines in the Sun’s spectrum

Absorption Line Spectrum

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Gustav Kirchhoff (1824-1887)

absorption lines of hydrogen

Emission Line Spectrum

• Produced by a low-density gas

• depends on composition and temperature

Emission lines

The Balmer series for hydrogen: Visible light

electrons falling to n=2

Rydberg formula (Balmer for nf = 2) :1 / = R (1/nf

2 - 1/ni2)

R = Rydberg constant = 1.097 x 107 m-1

The hydrogen atom

Energy levels and transitions of the many-electron atom: Sodium

Quantum states of the valence electron

The Bohr Model

• Classical physics predicts that the electron should spiral into the nucleus

• Cannot explain emission spectra

The Bohr model:•The e- stays in certain stable orbits, emits no radiation unless it jumps to a lower level

•The angular momentum of the e- is quantized

•the attaction between p and e- provides the centripetal acceleration

n = principal quantum number

From Coulomb’s law, the force between the proton and electron is

F = 1

40

q1 q2 r2

This is the centripetal force, mv2 / r

Where q1 = q2 = e for the hydrogen atom

Bohr radius a0 = 0h2 / me2 = 5.29 x 10-11 m

So when the electron is in any energy level n:

KE of the electron in the nth level: Kn = 1/2 mv2

-1

40

e2 r

PE of the electron in the nth level: Un =

Total energy En = Kn + Un = ??? Compare to Rydberg formula!

Reduced mass: the nucleus is not infinite in mass, Bohr model is off by 0.1%

mr = m1 + m2

m1 m2

isotopes

Ionized Helium is also a 1-electron atom

Why is the emission spectrum of ionized helium similar to that of hydrogen?

1. Because hydrogen and helium are similar chemically

2. Because several of the energy levels of hydrogen and helium are the same

3. Because hydrogen and helium have similar atomic masses

4. It is a total coincidence

Energy Level Transitions

AllowedNot Allowed

• Continuum• Ionization• Differences

between elements• isotopes

Stellar classification scheme

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Is this star hotter or cooler than the Sun?

Spectrum of Arcturus

Temperature

Lu

min

osi

tyThe Hertzsprung-Russell diagram plots the luminosity vs. temperature of stars

B - V is a measure of color: the smaller B-V, the hotter the star (magnitudes, remember!)

Lines in a star’s spectrum correspond to a spectral type that reveals its temperature

(Hottest) O B A F G K M (Coolest)