Investigating the Quantum Defect values for Lithium
Used a spectrograph to analyse the spectra of light from Lithium, with the aim of measuring the how far this differed from the Hydrogen model. This allowed us to see how the energy levels of Lithium differed from the prediction made by the basic Bohr model due to screening of the nucleus by the inner electron. Our results corroborated well with the accepted values and showed that the screening effect reduced when the outer electron was transitioned from higher levels. This was a very fiddly experiment, we had to use photographic film to capture the spectra from two temperamental carbon electrodes.
Investigating the Propagation of Electrical and Thermal Waves
This report consists of two separate experiments, both investigating the way waves propagate through different media. A square wave was sent into a transmission line (a series of capacitors and resistors), we discovered it was deformed as it traveled down the line. We later discovered this was because the transmission line acted as a low pass filter, so only low frequencies could pass through and the truncated Fourier series was the cause of the deformed shape. The line was also found to be dispersive, with different frequencies traveling at different speeds, creating even more deformation. We also set up a resonator by making both ends of the line reflective and found the Q value.
The second experiment saw the investigation of thermal waves through a PTFE cylinder. A square wave was created by transferring the cylinder between hot and cold water baths, and a thermometer inside recorded the same wave after passing through the material. We used Fourier methods to isolate the different frequencies and measure the attenuation. From this, we could calculate the thermal diffusivity, which differed slightly from the accepted value, which we attributed to an assumption we made to treat the cylinder as a plane slab (not really our decision but it made the maths a lot easier, didn't have to use Bessel Functions). I wrote this report with food poisoning, so pretty pleased with how it turned out.
Investigating Mercury and White Light Sources with a Michelson Interferometer
Used a Michelson interferometer to analyse the spectra of Mercury and white light, calculating the spectral width and wavelength of each light source. Our results did agree with the accepted values and more in depth discussion is seen in the report. The main feature of this report is the correction of the motor used to scan across the spectra. We noticed that the wavelength measured followed a sinusoidal pattern, we then measured the step size from a known wavelength of green light which showed the same pattern. So, in fact, the step size of the motor was not constant as we had assumed, so we corrected this error to reduce our error by 41%.
This lab cycle also had a section on Holography which was very interesting but we were advised not to write a report on it. However, I can show you the holograms we made of a coin and a key as seen below. We also created a holographic lens which could focus light even though it was two dimensional.
Modelling the Kinetic Theory of Gases
This was a Python project, so to see the code and animation in more detail visit Year 2 code. So the code simulates a gas and it records pressure, temperature and volume. This allowed for the testing of various gas laws, and I found that for large volume particles the ideal gas law was no longer applicable and Van der Waals equation of state must be used because of the reduced volume available to the gas. I also simulated Brownian motion by making one ball larger than the others, the path of the larger ball was used to show a random walk with a smaller mean free path than the other particles. The distribution of velocities was also plotted and matched the Maxwell-Boltzmann distribution as expected.