Revolution of Modern Physics (2)

In a former post, I described two experiments: the photoelectric effect and the black body radiation. I finish the topic in this post by explaining three more experiments:

3) Frank-Hertz experiment

The experiment of Franck and Hertz consisted of bombarding atoms with monoenergetic electrons and measuring the kinetic energy of the scattered electrons. The amount of the energy absorbed in the collision can thus be estimated. SupposeE₀, E₁, E₂, … are the sequence of quantized energy levels of the atom and and T is the kinetic energy of the incident electron. As long as T is below ∆=(E₁– E₀), the atoms cannot absorb the energy and all collisions are elastic. As soon as T>(E₁– E₀), inelastic collisions occur and some atoms go into their first excited states. Similarly, atoms can be excited to second and higher excited states. Thus Frank-Hertz experiment established the quantization of the atomic energy levels.

4) Davisson-Germer experiment

L. de Broglie, seeking to establish the basis of a unified theory of matter and radiation, postulated that matter, as well as light, exhibited both wave and particle aspects. The first diffraction experiments with matter waves were performed with an electron beam by Davisson and Germer (1927). The incident beam was obtained by accelerating  electrons through an electric potential. Knowing the parameters of the crystal lattice, it was possible to deduce an experimental value for the electron wavelength. The result was in agreement with de Broglie  relation, λ=h/p, where h is Planck’s constant and p is the momentum of electron. Similar experiments were later performed using beams of hydrogen molecule and helium atoms. Hence, it showed the wavelike nature of matter.

5) Compton scattering

Compton observed the scattering of X-rays by free or weakly bounded electrons and found the wavelength of the scattered radiation exceeded that of the incident radiation. The difference, ∆λ,  varied as a function of the angle θ between the incident and scattered directions:

where h is the Planck’s constant and m is the rest mass of the electron. Furthermore, ∆λ is independent of the incident wavelength. The Compton effect cannot be explained by any classical theory of light. Hence, it is a confirmation of the photon theory of light.

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Revolution of Modern Physics (1)

In late 19th and early 20 century, a few physical experiments changed our understanding of the nature fundamentally. Later, they led physicists to Quantum mechanics. In this post, I give a brief overview of the most important experiments.

1) Photoelectric effect

This refers to emission of electrons observed when one irradiates a metal under vacuum with ultraviolet light. it was found that the magnitude  of the electric current thus produced is proportional to the intensity of the striking radiation provided that the frequency of the frequency of the light is greater than a minimum value characteristic of the metal, while the speed of electrons does not depends on the light intensity, but on its frequency. These results could not be explained by classical physics.

Einstein in 1905 explained these results by assuming light, in its interaction with matter, consisted of packets of energy hν,called photon energy. when a photon encontures an electron of the metal it is entirely absorbed, and the electron, after receiving the energy hν, spends an amount of work W equal to its binding energy in the metal, and leaves with a kinetic energy of

½ mv² = hν – W

This quantitative theory of photoelectrons has been completely verified by experiment, thus establishing a quantum nature of light.

2) Black body radiation

A black body is one which absorbs all the radiation falling on it. The spectral distribution of the radiation emitted by a black body can be derived from the general laws of interaction between matter and radiation. The experissions deduced from the classical theory are known as Wien’s law and Rayleight’s law. The former is a good approximation in the short wavelength part of the spectrum, while the latter is in agreement with long wavelength experiments but leads to infinite total energy.

Planck in 1900 succeeded in removing the discrepancy by postulating that energy exchanges between matter and radiation do not take place in a continuous manner but by discrete quantities of energy. He showed that by assuming that the quantum  of energy was proportional to the frequency, ε = hν, the expression of the spectrum, in agreemnet with experiments, is 

where h is a universal constant, known as Planck’s constant. Planck’s hypothesis was confirmed by a set of experiments. Note that in the limit of short and long wavelengths, this equation with reduce to the Wien/Rayleigh forms.

In the next post, I describe the following three expriments:

3) Frank-Hertz experiment

4) Davisson-Germer experiment

5) Compton scattering

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Natbib: change spacing in references

It happens that you would like to decrease the spacing in your references, e.g. for a thesis. Here, I found a simple way how to do it. Add the following to your preamble (the body of LaTEx program before \begin{document}):

\let\oldthebibliography=\thebibliography
\let\endoldthebibliography=\endthebibliography
\renewenvironment{thebibliography}[1]{%
\begin{oldthebibliography}{#1}%
\setlength{\parskip}{0ex}%
\setlength{\itemsep}{0ex}%
}%
{%
\end{oldthebibliography}%
}

It worked for me, so I hope works for you as well. If you do NOT use Natbib, you have to solve the problem differently.

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Photography of lunar eclipses

It can be a lot of fun to capture some photos from astronomical event. In this post, I explain how to do so for a lunar eclipse since a great total lunar eclipse is coming.

Assumptions: you have a tripod, a (digital) SLR camera, and perhaps a cable release. That means you do NOT need any dedicated astronomical telescope for this purpose.

If you are going to shoot some photos from the eclipse, there are some simple tricks you can keep in mind. First of all, use a tripod and cable release to avoid shaking. Second, try a few different exposures to make sure you neither over expose nor under expose the photos. These two points also apply to solar eclipse photography. The exact setup of the f/ratio and exposure depends on the darkness of the eclipse.  Since this eclipse will be probably a dark one, I guess I try the followings:

F/ratio : a fast optics like f/5.6 or f/4.0 is always good in astrophotography. If maximum opening of your objective is like e.g., 5.6, close it one more step to have a better optical quality.

Exposure : with current digital cameras, you can check the histogram (intensity distribution) of the captured frame immediately. The distribution should have a mean value about the half of the depth of your chip pixels. For instance if your camera has a 12 bit chip (like mine), you have a full well depth of 2 to power 12, which is 4096. In this example, a histogram which peaks about 2000 is good. Also note that you should avoid overexposing: i.e., the histogram tail toward larger values should NOT touch the very end. In brief, use both visual inspection of the photo and histogram to make sure you have the right exposure time.

All in all, try exposures like 1/15 to 1/125 sec for the partial eclipse. Take one or two more exposures with one step more or less to make sure you captured everything.  To record the Moon during totality, you need a few seconds of exposure depending on the darkness of the eclipse. Unlike a solar eclipse, you have plenty of time. So check the captured frames to be 100% on the safe side.

ISO : I usually use 800 or 400. It actually depends if the selected sensitivity in your camera is too noisy or not. If you are doubtful, take ISO 400 as initial guess. The higher the sensitivity, the lower the difference between the maximum and minimum in your Photo. Therefore, a medium ISO value keeps both the dynamic range and the chip sensitivity.

Focal length : as long as you can. If you have a tele lens of F=100 to 300 mm, try that. Be careful about the f/ratio of tele lenses. You might have a very long focal length lens like F=500mm or more but with a f/ratio like f/8 or even worse. In this case, you have to increase the exposure time.

Focus : that is the master key for astrophotography.  Never underestimate the importance of a great focus. Invest enough time in advance to focus your system.

Camera settings : if you have a digital SLR camera, you can check  this link to adjust general settings of your camera. For instance, you should use the maximum resolution of the camera.

Telescopic observations : if you have a telescope and a digital SLR camera or a CCD, you can of course take advantage of them and record great photos. The long focal length of a telescope will allow you to capture details that cannot be recorded with normal photography. Get the proper T-mount and adapters to connect your camera (body) to the telescope (the prime focus method).  This way, the image that forms in the focal plane of the optical system will be on the chip of the camera.  The telescope then acts as a camera lens. That is an easy way for telescopic astrophotography. You can use other methods of attaching a digital camera or CCD to a telescope for larger magnifications as well. I try to explain details of this method in a separate post.

I wish you a nice weather condition, a great seeing, and perfect photos !

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