AIMS The goal of the Franck-Hertz experiment is to demonstrate that electrons occupy only discrete, quantized energy states for neon and argon atoms.

Common signal processing tasks in the numerical handling of experimental data include interpolation, smoothing, and propagation of uncertainty. A comparison of experimental results to a theoretical model further requires curve fitting, the plotting of functions and data,  and a determination of the goodness of fit. These tasks often typically require an interactive, exploratory approach to the data, yet for the results to be reliable, the original data needs to be freely available and resulting analysis readily reproducible. In this article, we provide examples of how to use the Numerical Python (Numpy) and Scientific Python (SciPy) packages and interactive Jupyter Notebooks to accomplish these goals for data stored in a common plain text spreadsheet format. Sample Jupyter notebooks containing the Python code used to carry out these tasks are included and can be used as templates for the analysis of new data. 

AIMS The Faraday Rotation of Polarized light is the rotation of the plane of polarization of light propagating through a medium due to the presence of a magnetic field. In this experiment, we aim to measure the Verdet constant of a glass rod (SF-57) through the Faraday Effect.

ABSTRACT The lowest excitation energy of the elements Neon, Mercury, and Argon was determined by analyzing the fundamental properties of the signal structure in the Franck-Hertz experiment. In order to accurately determine the lowest excitation energy a new method proposed in was employed. The main idea is that the spacings between the minima in the Franck Hertz curve increase linearly due to the additional acceleration over the mean free path. Therefore a linear fit was applied to graphs of spacings ΔE versus minimum order n. The fit estimated the lowest excitation energies of Neon (19.54 ± 1.48eV), Mercury (4.72 ± .25eV), and Argon (11.36 ± .38eV) accurately within experimental uncertainty.

AIMS The goal of the Franck-Hertz experiment is to demonstrate that electrons occupy only discrete, quantized energy states for neon and argon atoms.

ENERGY CONSERVATION IN SWEPT FIELD LIMIT For a calorimeter sample (plus addenda) weakly thermally linked to a temperature controlled reservoir, energy conservation implies -T dS = \kappa \Delta T dt + C_{} dT where κ is the sample to reservoir thermal conductance and addenda is the heat capacity of the actual addenda (such as the thermometer, heater, and glue or grease binding the sample to the sensors) plus the heat capacity of the sample lattice (due to phonons). The left hand side term is the heat released by the system — which in the case of a spin system, for example, would be the heat released by the spins — when the field is changed by dH. The minus sign indicates that system entropy decreases as heat is released. Most of the released heat flows to the reservoir but some fraction heats up the addenda (to the same temperature as the system). The first term on the right hand side describes heat flow to the reservoir. The second term describes the temperature rise of the addenda. In a non-adiabatic relaxation-time or ac-calorimeter like that used in our swept-field measurements , the first term dominates. In contrast, in an adiabatic measurement, the first term is negligible.

We examined the relationship between magnetization, polarizing field time, magnetic field and precession frequency using a 125 mL sample of water and the TeachSpin Earth’s Field NMR instrument. Through varying these different parameters, we could determine the Larmor precession frequency of protons within Earth’s field, spin-lattice relaxation time, and the gyromagnetic ratio for protons. We found the Larmor precession frequency to be 1852 ± 18 Hz corresponding to a local magnetic field of 43.3 ± 0.3μT due to Earth’s magnetic field, the spin-lattice relaxation time to be 2.15 ± 0.05 s, and the gyromagnetic ratio to be $(2.65\pm0.04) \cdot 10^8~{s\cdot T}$, agreeing with the known value of $2.68\cdot 10^8~{s\cdot T}$.

Two sources of noise, Johnson noise and shot noise, are investigated in this experiment. The Johnson noise, which is the voltage fluctuations across a resistor that arose from the random motion of electrons, is measured using the Noise Fundamentals box. The noise was measured across different resistances and at different bandwidths at room temperature, resulting in a calculation of the Boltzmann constant of 1.4600 ± 0.0054 ⋅ 10−23 m² kg s−2 K−1 and 1.4600 ± 0.0052 ⋅ 10−23 m² kg s−2 K−1. The shot noise occurs due to the quantization of charge, and was measured by varying current in the system, with which we calculated the electron charge of 1.649 ± 0.007 ⋅ 10−19 Coulombs. They agree quite well with the accepted values of 1.38064852 ⋅ 10−23 m² kg s−2 k−1, and 1.64 ⋅ 10−19C for the Boltzmann constant and electron charge respectively. Errors are discussed.

AIMS The Faraday Rotation of Polarized light is the rotation of the plane of polarization of light propagating through a medium due to the presence of a magnetic field. In this experiment, we aim to measure the Verdet constant of a glass rod (SF-57) through the Faraday Effect.

ABSTRACT We performed an experiment to measure the Faraday rotation of polarized light passing through a magnetic field, as well as measuring the Verdet constant of an SF57 glass tube with a length of 0.1 m. Our results are consistent with the general idea of Faraday rotation, which suggests that linearly polarized light experiences rotation when applying a magnetic field. We used three different methods to find Verdet constants, which are Direct Fit, Slope Fit and Lock-in Method. The values we found are $21\pm 5 {T \cdot m}$, $21.095\pm0.003 {T \cdot m}$ and $20.43\pm0.06 {T \cdot m}$ respectively, and those values are consistent with each other within uncertainty.

We examined the relationship between magnetization, polarizing field time, magnetic field and precession frequency using a 125 mL sample of water and the TeachSpin Earth’s Field NMR instrument. Through varying these different parameters, we could determine the Larmor precession frequency of protons within Earth’s field, spin-lattice relaxation time, and the gyromagnetic ratio for protons. We found the Larmor precession frequency to be 1852 ± 18 Hz corresponding to a local magnetic field of 43.3 ± 0.3μT due to Earth’s magnetic field, the spin-lattice relaxation time to be 2.15 ± 0.05 s, and the gyromagnetic ratio to be $(2.65\pm0.04) \cdot 10^8~{s\cdot T}$, agreeing with the known value of $2.68\cdot 10^8~{s\cdot T}$.

ABSTRACT We performed both Doppler and subDoppler spectroscopy on the 5²S1/2 → 5²P3/2 transition of rubidium 85 (⁸⁵Rb) and rubidium 87 (⁸⁷Rb). We fit the Doppler spectroscopy curves to Maxwell Boltzmann velocity distributions to determine the temperature of the cell. We also fit the subDoppler spectroscopy curves to extract the transition energies and hyperfine structure of the 5²S1/2 F=2 ground state to the 5²P3/2 F=1, F=2, and F=3 excited states of ⁸⁵Rb, the 5²S1/2 F=3 ground state to the 5²P3/2 F=2, F=3, and F=4 excited states of ⁸⁵Rb, the 5²S1/2 F=1 ground state to the 5²P3/2 F=0, F=1, and F=2 excited states of ⁸⁷Rb, and the 5²S1/2 F=2 ground state to the 5²P3/2 F=1, F=2, and F=3 excited states of ⁸⁷Rb. The calculated difference between the transition from the F=2 excited state of the 5²S1/2 state of rubidium 87 to the 5²P3/2 state and the transition from the F=3 excited state of the 5²S1/2 state of rubidium 85 to the 5²P3/2 state, was found to be 1.062x10⁹ Hz ± 1.6x10⁷ Hz, compared to the value from of 1.22039x10⁹ Hz ± 2x10⁴ Hz. Our results for Doppler Spectroscopy were not quite consistent with theory within uncertainty, but there are many possible reasons for this slight discrepancy. The uncertainty in the Doppler profile fitting is most likely due to an incomplete model of the transmission curve. While we modeled the as a Maxwell Boltzmann Gaussian distribution, the actual curve is a convolution between the six Lorentzian line profiles and the Gaussian distribution. The uncertainty in the hyperfine fitting is likely mainly due to the fact that we modeled our frequency scan as linear but it is not actually linear.

Cosmic particles are found everywhere in the Universe from various high and low energy interactions. Muon and Gamma decay are two of the most frequent decays studied because muons are one of the most common particles and gamma rays are found everywhere in the Universe from many different type of radioactive decays. We used scintillators in order to produce the two different decays. For the gamma decay, the goal was to find an unknown radioactive sample and to find the different ages of two Cesium-137 samples by using Cesium-137 and Cobolt 60 to calibrate the energies. After analysis, we found that the unknown sample given to us was Sodium-22. We also found that one of the Cesium-137 samples was 17.583 years old and the other was 37.80 years old. The goal for the muon decay was to analyze long term data to see if we could calculate the time dilation effect commonly calculated using muons.

Ever since astronomers have been studying galaxies and their mass/luminosity relationship, there is clearly something wrong. There is a missing luminosity problem - there is a lot of non-luminous (about 90%) matter in a galaxy. Possible dark matter candidates come from cold dark matter, warm dark matter, hot dark matter, and axions. After years of research, astronomers and physicists can rule out warm and hot dark matter, but cold dark matter and axions are both extremely probable candidates of dark matter. In this report, I will explain about all the different candidates of dark matter and their implications.

Planets absorb energy as light from stars and radiate energy out in to space at a rate that increases with temperature, allowing it to keep in balance, at some equilibrium temperature, when the energy gain equals the energy loss.

ABSTRACT We performed an experiment to measure the Faraday rotation of polarized light passing through a magnetic field, as well as measuring the Verdet constant of an SF57 glass tube with a length of 0.1 m. Our results are consistent with the general idea of Faraday rotation, which suggests that linearly polarized light experiences rotation when applying a magnetic field. We used three different methods to find Verdet constants, which are Direct Fit, Slope Fit and Lock-in Method. The values we found are $21\pm 5 {T \cdot m}$, $21.095\pm0.003 {T \cdot m}$ and $20.43\pm0.06 {T \cdot m}$ respectively, and those values are consistent with each other within uncertainty.

ABSTRACT An electromagnet was used to provide a magnetic field to 3 different conducting samples: n type Geranium (n-Ge), p type Geranium (p-Ge), and silver (Ag). A calibrated Hall probe was used to obtain the current ($_{mag}$) to magnetic field ($$) calibration of the iron-core electromagnet. The Hall voltages (VH) produced by each of the three samples were plotted against B, and a linear line was produced, as expected. The slope (${\Delta B}$) of each of the graphs were used to calculate the Hall coefficient for each sample, which we found to be $-4.99\cdot 10^{-3}\pm -0.0998 \cdot 10^{-3}}{}$, $5.64 \cdot 10^{-3}\pm 0.11 \cdot 10^{-3} }{}$, $-2.24 \cdot 10^{-10}\pm -0.04 \cdot 10^{-10} }{}$ respectively. These do not really agree with given values of $-5.6\cdot 10^{-3}}{}$ for n-Ge, $6.6\cdot 10^{-3}}{}$ for p-Ge, and $-8.9\cdot 10^{-11}}{}$ for silver by the manufacturer. Using the Hall coefficients, we found their carrier densities to be −1.25 ⋅ 10²¹ ± 0.025 ⋅ 10²¹m−3 for n-Ge, 1.11 ⋅ 10²¹ ± 0.02 ⋅ 10²¹m−3 for p-Ge, −2.79 ⋅ 10²⁸ ± 0.06 ⋅ 10²⁸m−3 for silver, which are all in the same order of magnitude as the given absolute values of 1.2 ⋅ 10²¹m−3, 1.1 ⋅ 10²¹m−3, 6.6 ⋅ 10²⁸m−3. A current was applied to the superconductor Bi₂Sr₂Ca₂Cu₃O₁₀ which was cooled in liquid nitrogen until it became superconducting, and was allowed to warm slowly. Its voltage and temperature were monitored in the warming process which we used to produce a graph of voltage against temperature. The graph showed a transition temperature of about 118K ± 2K, similar to the provided critical temperature of 108K.

How can we use thermodynamics to understand the structure of our atmosphere?