Emission Spectrum of Hydrogen Discrete Not Continuous

Lecture 6: Discrete Spectra of Atoms

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Three types of Spectra

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Kirchhoff's Laws Continuous (or blackbody) spectrum occurs when we look directly at a hot opague source. Emission line spectrum occurs when we look at a transparent gas which is being excited by the blackbody source, but we can't see the source directly. Absorption line spectrum occurs when we look at a cool layer of gas which blocks a blackbody source and absorbs the blackbody photons.

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Atomic Spectra: Fingerprints of Atoms

• Each element has a unique set of energy levels where electrons can orbit.

• Each element has a unique set of coloured spectral lines which can be used to identify the element.

• Not all of an elements spectral lines will correspond to EM waves in the visible part of the spectrum.

• for example

• Absorption and emission spectral lines are at exactly the same wavelengths. What you see is determined by environment.

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Astronomy: A Hydrogen Emission Nebula A hot star sits inside this cloud of gas (called a nebula) UV photons emitted by the star excite the atoms in the gas. The electrons jump back to the ground state, emitting light with the colours typical for that atom. In this case, the gas is mostly Hydrogen, so most of the light emitted is the red Balmer alpha light and the nebula glows pinkish-red. Since Hydrogen is the most common element in the Universe, most emission nebulae are red.

Astronomy: The Sun's Absorption Spectrum

The Sun's spectrum is an absorption line spectrum. The spectral lines give us the chemical composition of the Sun's atmosphere. (Mainly Hydrogen)

Some fun links to research-quality Solar spectra:
Interactive Solar Spectrum
Complete Solar Spectrum from 380 to 870 nm

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Hydrogen's Spectrum

Lyman Series When an electron jumps from an excited state to the ground state n=1 an Ultraviolet photon is emitted. These ultraviolet spectral lines are called the Lyman series . and denoted Ly&alpha, Ly&beta, Ly&gamma ... Balmer Series When an electron jumps from an excited state to the n=2 state a Visible photon is emitted. The jump down to n=2 is called Balmer series, with the lines H&alpha, H&beta, H&gamma ... The Balmer alpha photon is red (wavelength = 656 nm)

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Let us practice some computations

We need the following constants

c=3.00 x 108 m

h=6.63 x 10-34 J.s

kB=1.38 x 10-23 J/K

R = 1.10 x 107 m-1

1 eV = 1.60 x 10-19 J

and formulas
Ly-alpha line with longest wavelength ?

Minimum energy to excite hydrogen atom ?

Which jump between close levels is in visible range ?

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Hydrogen's Spectrum Balmer lines

Name	Initial State	Final State	Colour	Wavelength
Balmer alpha	3	2	red	656 nm
Balmer beta	4	2	green-blue	486 nm
Balmer gamma	5	2	blue	434 nm
Balmer delta	6	2	violet	410 nm

Interactive Solar Spectrum: can you find Balmer lines ?

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Doppler Shift

Waves in water, air ... Stationary source produces waves with constant wavelength in all directions. If the source is moving then the observer sees that: wavelength is shorter in the direction which the source moves ; wavelength is longer in the direction opposite to the source motion .

Useful animations 1, 2

• The change in the wavelength is related to the relative velocity v between the source and the observer and is called Doppler shift given by the formula
  • In this equation c is the speed of the wave in the medium.

Electromagnetic waves (light):

• The Doppler shift holds for all types of waves including:
  • sound waves (eg. ambulance). Here "c" is speed of sound
  • light waves. Here "c" is speed of light.

• Formula for Doppler shift is the same for light, but physics is different - special relativity.

Doppler effect is extremely useful:

• If you can measure the shift in wavelength of a star's spectrum relative to lab you can determine the star's velocity relative to you!

• If you can measure the width of the spectral line in stellar spectrum caused by thermal motions of atoms, you can measure temperature of the star !

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Next lecture: Optics and Telescopes
Read Chapter 6

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Source: https://sites.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect6/lecture6.html