Monday, 21 December 2009

Bored of Bohr?

Hey Reader,
What is that weird word ion the title: Bohr? Well, here we are talking about the physicist, Neils Bohr, the man responsible for the High School model of the atom! You know, that model that mimics the solar system. How did it come about? Why is it useful? Why is it used?

To start, lets see the history of the atom and the models. It started with Dalton, when he stated that the atom is the smallest unit of matter. He also stated that the atom is just a solid ball (such as a billiard ball). This formed the first theory of the atom

Then came J.J. Thompson, who realized that a charge can be induced onto the atom. Negative or positive, there has to be a way to charge an atom. He devised a model (sometimes called the plum-pudding model) in which allows the charges of the atom to be spread-out in a "solid" atom.

50 years later, a famous experiment, called the Gold Foil experiment was performed by Ernest Rutherford. His discover shocked the world of science. He shot positive particles (alpha particles) through a thin gold foil and placed detectors at different angles. He observed that many alpha particles was deflected at very small angles. they almost
passed right through!. How could this be unless there was a central nucleus with a positive charge. Thus, we learned that there was a central positive nucleus.

Borh showed that electrons are in orbits. Shown above, electrons circle the nucleus like planets around the sun. The first orbit holds 2 electrons, the 2nd and 3rd each have 8. This is NOT what the current model represents, but this is widely used in many people's education.

This model is useful because it explains a weird phenomenon
. Certain elements emit a certain spectra of light. To the right is a small spectrum (known as the Balmer) that is emitted from Hydrogen. Hydrogen emit other visible lights as well. How can this be explained unless electrons can get excited to different orbitals and de-excited states to lower orbitals. To produce light, with this model, an electron must go from a higher orbital to a lower orbital (Blamer series goes from any higher orbital to the 2nd orbital). This can be mathematically explained using the Rydberg-Balmer equation. The wavelength is correlated to the difference of squared orbitals.

Even though a more accurate model has been discovered, called Valence Shell Electron Pair Repulsion (VSEPR) theory, Borh's model is a very basic model that works well with the spectral phenomenon. We use it so we can better understand the light.

Saturday, 19 December 2009

Momenergy != Mom Energy

Hello Reader,

I know, it's been too long since an actual update to this blog, which is bad on my part As a New Years promise to myself (I make promises and not resolution for the simple fact that I don't have much of a problem needing to be resolved), I will try my hardest to have 2 updates/postings a month. Now this may get extremely difficult, considering my course load is quite heavy. But I am going to try to do it anyways.

Now, you probably read the title and wondered if the one word up there is actually a word. No I did not mean "Mom Energy", this is a scientific word. What I mean is it's a word that was created from scientist to use instead of using "Momentum-Energy" because saying that 10 times fast would be just too darn difficult.

What is Momenergy? Well, it's just that, Momentum AND Energy in the same 4-D vector. Like Space-time's 4-D vector ( [t,x,y,z] , where time is scalar value by itself), Energy and momentum make up a 4 dimensional vector [E, p_x, p_y, p_z]. It is a branch off of Einstein's Theory of Special Relativity. But unlike Spacetime, where you can have 2 different units (light seconds for space or seconds for time), there is only 1 designated unit for momenergy, and that is kilograms! Let's dissect this a bit:

Let's start with Energy. Most people measure it in Calories because that's what's on the food packages. But the standard units of energy are Joules. 1 Joule is 1Kg x 1m/s/s (unit of acceleration) x 1 meter or 1 Kg x 1 m^2/s^2. Now, recall that c (the constant, the speed of light) is pretty much the basis of Einstein's Theory, nothing can go fast than it (with 1 exception that I know of). So it would seem appropriate to use this in the calculation to figure out relativistic energy. Remember that c is a speed so the units are m/s so if we square it, we get m^2/s^2 and if we multiply by mass, we get mc^2, the world famous physics equation. But for relativistic purposes, we are going to have gamma (stretch factor) multiplied by mass. The stretch factor is in units of c. So that everything cancels nicely and we get only the units of mass left.
1/c * c * kg = kg

The same can be done for momentum because it's classical units are kg * m/v. But, here you will multiply together, the stretch factor, the mass and the relativistic speed. Everything still cancels out to kg!

These values when you use Lorentz geometry, will give you the rest mass of an object. These also play a role in the Uncertainty Principle. There are 2 forms to this principle, the momentum-space and the Energy-Time. It states that you cannot know both of these values simultaneously with extreme accuracy. So you either know Energy really well but not the time or you know Time with great accuracy and not the energy (this is on the atomic level).

Stay tuned for more stuff in the near future!