deletions | additions       diff --git a/In_order_to_create_these__.tex b/In_order_to_create_these__.tex  index 511d9be..d30dd37 100644  --- a/In_order_to_create_these__.tex  +++ b/In_order_to_create_these__.tex 
...
In order to create these particular circumstances in the experimental arrangement arrangement,  two grids are placed between an electron-emitting cathode (filament) and an anode used for electron collection. The beam is accelerated between the cathode and grid 1 ($G_{1}$), then bombards atoms of the element between grid 1 and grid 2 ($G_{2}$). In the set-up used for Neon and Argon, a small voltage, $U_{1}$, is applied between the cathode and grid 1 in order to control the emission of electrons. This voltage is not critical to the experiment, thus in the experimental set-up for Mercury, grid 1 is absent. In order for the electrons to gain enough energy to collide inelastically with atoms of the vapor, an accelerating voltage $U_{2}$ is present between $G_{1}$ and $G_{2}$. A retarding voltage $U_{3}$ between $G_{2}$ and the anode prevents electrons that have lost most of their energy ($  \par To observe the current minimas in Argon, $U_{2}$ was varied from $0V-100V$ in increments of either $0.1V$ or $0.01V$. Increments of $0.1V$ were used for the accelerating voltage when the data was not at a peak or dip, and increments of $0.01V$ were used for the accelerating voltage when the current was at a minimum value, again in hopes of resolving fine structure. The high power voltage amplifier (x20 gain) was also used in the experimental set-up for Argon, and again was applied between $G_{1}$ and $G_{2}$ in order to amplifying the value of accelerating voltage. It is also important to note that dips are not perfectly sharp, due to the of the lifetime of each excited state, and due to the distribution of velocities for emitted electrons. It is also generally assumed that all maxima and minima spacings in the Franck-Hertz curve correspond to the first excitation energy of atoms. Though it was previously thought that these dips were equidistant to one another, more recent studies \cite{Rapior_2006} have shown that the distance between successive points increases linearly. Furthermore, the energy spacings between consecutive dips depends on whether or not the mean free path, $\lambda$, is large enough to be significant. Since $\lambda$ is defined to be the average distance an electron moves before an inelastic collision takes place, $\lambda$ should be shorter in higher density gases, since atoms are more closely packed together. Mercury, Neon, and Argon are all relatively low density gases, thus the mean free path is large enough to be significant, and the energy spacing between consecutive dips should increase linearly. Plots of the linearly increasing distances between these points were analyzed in order to determine excitation energy for the lowest state for all three elements.