Category: 18 Quantum Physics

104 High Pressure Sodium Lamp

There are many interesting features in the spectrum of light emitted by a high pressure sodium (HPS) lamp.

Most of the blue lines are emission lines from mercury.

The dominant light of the HPS lamp comes from the yellowish sodium D-line. In low pressure sodium lamp, the D-line would have been a narrow discrete line (a doublet actually). But in HPS lamps, this line is broadened so much by high pressure that it appears like a continuous spectrum. This broadening is caused by the emitting atoms suffering collisions during the emitting process. Because the collision time is much shorter than the lifetime of the emission process, the uncertainty in the energy emitted is increased (Heisenberg Uncertainty Principle, ΔE Δt > h/4π).

Notice also the dark absorption line in the pressure broadened sodium D-line. This is due to absorption by the cooler sodium at the outer layers of the lamp. Because the probability of absorption is much higher near the line centre than at the wings, the sodium D-line undergoes a self-reversal near the line centre.

Sources:

http://en.wikipedia.org/wiki/Sodium-vapor_lamp

http://en.wikipedia.org/wiki/Spectral_line

103 Electron Diffraction

The electron diffraction experiment demonstrates the wave nature of electrons. An electron with momentum p has a de Broglie’s wavelength of λ=h/p. When a beam of electrons is passed through a crystalline structure (such as graphite), an interference pattern of bright and dark rings is formed. If the electrons are accelerated to higher momentum (by turning up the accelerating voltage), the electrons’ wavelength will decrease. The separation between the bright and dark rings will thus decreases. (similar to fringe separation in the double slit experiment being dependent on wavelength Δy=Lλ/d)

102: Solar Spectrum

The sun’s core emits a continuous spectrum of light. However, the gas atoms in the sun’s “atmosphere” are capable of absorbing some of this light. Thanks to the discrete energy levels in gas atoms, these gas atoms can only absorb photons of certain energies (and since E=hc/λ, photons of certain wavelengths) that match the energy gaps in the energy levels of the gas atoms (|E2-E1|= hc/λ), resulting in dark lines in the solar spectrum at those wavelengths.

Capture

Out of curiosity, I tried to match the absorption lines in my video to those published on the internet (see http://en.wikipedia.org/wiki/Sunlight). With a little confidence, I think four of the more prominent dark lines (labelled C, D, E and F) in the spectrum are due to absorption by Sodium, Iron, Hydrogen and Iron atoms in the Sun’s atmosphere.

P.S.

It came as a surprise to me that the absorption lines of the solar spectrum can be viewed directly with the naked eyes using a grating. Although the video camera tends to over exposure the image (thus resulting in the absorption lines being washed out), the dark lines are clearly visible momentarily when the camera was in the midst of “correcting” the exposure.

Crookes Radiometer — xmdemo 080

Clearly, the “lightmill” rotates faster if more light hits it. Light bulbs behave like point sources in the sense that energy is propagated uniformly in all directions. So the intensity of light should roughly decrease with the square of the distance. This is why there was such a big difference in the rotating speed among the three lightmills. When both light bulbs were switched on, the resulting intensity profile is reminiscent of the electric potential between two positive charges.

So why do the radiometers rotate at all? There are two popular (but wrong) explanations.

Many people think that the light hitting on the vanes impart a momentum on them. Photons have no mass but they do possess (de Brogile’s) momentum. However, the problem with this explanation is, the photons bouncing off the bright surfaces should impart more momentum (through elastic collisions) to the bright surfaces. The photons being absorbed by the dark surfaces should impart less momentum (through inelastic collisions) to the dark surfaces. This explanation predicts the radiometer rotating with the dark surfaces leading, which is the opposite of the observed behavior of the radiometer!

Another equally popular but wrong explanation goes like this. The dark surfaces are warmer than the bright surfaces, causing the air to be hotter near the dark surfaces than bright surfaces. The higher pressure on the dark side (compared to the bright side) rotates the radiometer with the bright surfaces leading. Unfortunately, this explanation is flawed because higher temperature need not always result in higher pressure. In fact, we expect the air to be cooler but denser on the bright side. So even though the air molecules are less energetic individually, there are more of them, making the pressure as high as the dark side, which have more energytic but less number of molecules. In fact, the pressure in the radiometer should be uniform throughout even though there is a temperature gradient between a dark and bright surface.

The currently accepted explanation is based on something called thermal transpiration. Since I have no idea what it is, I will not write about it.

Further reading: http://en.wikipedia.org/wiki/Crookes_radiometer

037 Incandescence, LED and Fluorescent Spectrum

This video showcases the spectrum produced by three different types of lighting.

(1)

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A tungsten filament glows because of electromagnetic radiation generated by the thermal motion (more specifically, acceleration) of charged particles. Production of light in this manner is called thermal radiation or incandescence. Since there is a continuous range of thermal motion, incandescence produces a continuous spectrum.

(2)

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LED is a p-n junction that emits photons when conduction band electrons recombine with valence band holes. The energy (and thus wavelength) of the photon is equal to the energy transition made by the electron. This is kind of similar to how light is produced in a gas discharge lamp. However, unlike a gas atom where transitions are between discrete energy lines, in the p-n junction the transitions are between the conduction band and valence band. The spectrum of a LED light is thus not discrete, but centred about the band gap energy.

(3)

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A fluorescent tube is like a improved  mercury discharge tube. Unlike a mercury vapour lamp where a lot of energy is wasted in the ultra-violet light produced, a fluorescent tube is coated with a fluorescent coating. The fluorescent molecules are excited by ultra-violet photon from ground state to one of the vibrational states in the excited states. When they de-excite (through collisions with other molecules), they emit a few visible photons as they cascade from the vibrational states. As a result, the spectrum of a fluorescent lamp consist of both the discrete lines due to the mercury vapour and a continuous spectrum due to fluorescence. The choice of fluorescent material gives rise to different flavors such as warm white, cool white, daylight, etc.

036 Line Emission Spectral

The light from the Sun, a filament lamp, a candle flame, produces a continuous spectrum. The light from a gas discharge lamp however produces a discrete line spectrum.  For example, the hydrogen gas atoms emit visible light of wavelength 656.3 nm, 486.1 nm, 434.0 nm, 410.2 nm, 397.0 nm, 365 nm (called the Balmer series), and nothing in between. Why?

hydrogen_spectrum

It turns out that the electrons in a gas atom can only exist at certain energy levels. As a result, when the gas atom is excited (by the high voltage in the gas discharge tube), an electron in the atom can only be excited occupy not just any energy level, but only certain allowed energy levels. Subsequently, when the electron de-excites from a higher energy level to a lower energy level, a photon is emitted. And the energy of the photon is equal to the difference in the energy levels.

Since the energy levels are discrete, the electrons cannot de-excite from any energy level to any energy level. They can only de-excite from one of the allowed energy levels, to another of the allowed energy levels. As a result, only photons of certain energy levels, are emitted. Since E=hf, it follows that only light of only certain frequency and wavelength (E=hf), are emitted.