07.08.2010Lect. 5, gratings&light, 07.08.20101 CAPSTONE Lecture 5: Radiation from atoms

07.08.2010 Lect. 5, gratings&light, 07.08.2010 1

CAPSTONE Lecture 5:

Radiation from atoms


Radiation, Gratings

Light brings most of our knowledge about stars.

Waves have the property that they can be made to interfere.

Popsicle sticks in pools, boat wakes crossing, etc.

Light striking a grating leads to interference behind (transmission) or in front (refection) of the grating.

The more grooves, the higher the dispersion.

nm=sin 1 + sin 2: n=no. of grooves per mm; m= order number; lambda=wavelength; angles are of incidence and diffraction.

Use of hand held gratings in class.

Interference.


SpectraBlue light is closer to grating “zero order”

Multiple orders, m.

Each 2 has a color associated with it.

1 the same for all colors (incident light).

The entrance slit restricts all light to one angle (otherwise, the output makes no sense).

Wavelength of known lines will be slightly greater or less depending on the relative motion of the emitting object toward us. Called the Doppler shift.

=v/c. Motion toward us makes a blue shift (negative): motion toward us is defined as negative, away, as positive.


Emission lines from gases.Pure gases that are excited generate isolated emission lines with no light in between

Hot objects that are not pure emit a spectrum called “black body” radiation that is continuous, including all colors of the rainbow, as well as light at shorter and longer wavelengths than the eye can see.

The emission lines sometimes form regular patterns, especially in the case of hydrogen. Balmer observed these in 1885. He round a mathematical relationship in terms of wavelength: 1/=R[(1/n1)2-(1/n2)2]

R is the Rydberg constant, 109,000 cm-1.

If he assigned n1 to be 2 and assigned each line (n2) to integers 2,3,4, …he found that he could exactly calculate the wavelengths of all the lines.

In 1913, Bohr derived this equation from first principles, just as Newton did for Kepler’s empirical laws of the Solar System.


Theory of atomic spectra

Narrow lines from pure gases imply that specfic energy levels are involved. Bohr built a model for hydrogen in which electrons (negative) orbited protons (postive) under an inverse square force (electric field, but of the same form as the gravitational force). More tightly bound electrons are closer in and have more negative energy (“bound”). When an electron is removed, it is “free”. If an electron goes from a more distant orbit to a smaller orbit, the atom is in a more negative total energy state (potential energy) and some energy has to be released to balance that change. Light is emitted as a result. The energy of the light is just the energy difference of the levels involved: E=E(start)-E(end),

E=hhc/evx10-12 g-cm2/sec2 =x10-12 ergs


Absorption Lines

If an electron in a bound atomic energy level interacts with an incoming photon of exactly the right energy, the photon will be absorbed and the energy will go into increasing the energy of the electron (making it less tightly bound, in a outer electron orbit). Energy is conserved. The electron will then spontaneously decay to an inner orbit (lower total energy, more negative, more tighly bound), producing positive, balancing energy by emitting a photon of the same energy and wavelength as the one initially absorbed. ONLY discrete energies can lead to absorption or emission from bound levels.


Stellar and Interstellar Absorption Lines

In general, black body radiation produces photons of a wide range of energy, including higher energies for hotter objects. These photons can then be absorbed by atoms or ions (nuclei without a full set of electrons) that are between us and the black body (star), in discrete energies corresponding to energy separations.

There are other means of continuous energy emission, such as “Bremstrahlung”, acceleration of electrons by passing protons in hot gases, and synchrotron emission (radiation from high energy electrons, beamed by special relativistic effects).


Units

Atoms are of order 10-8 cm in size, or 1 Angstrom.

The energies between energy levels in atoms are typically a few electron volts, which corresponds to photon energies of 1000A to 10,000A, or 10-5 to

10-4 cm. The latter is 1 micron or 10-3 mm.

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07.08.2010Lect. 5, gratings&light, 07.08.20101 CAPSTONE Lecture 5: Radiation from atoms