deletions | additions       diff --git a/The_distance_the_electron_travels__.tex b/The_distance_the_electron_travels__.tex  index e6b7837..2a1cda3 100644  --- a/The_distance_the_electron_travels__.tex  +++ b/The_distance_the_electron_travels__.tex 
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As the applied accelerating voltage increases, electrons continue to gain energy along their mean free path and could possibility also excite the higher energy levels of the atoms. Since electrons gain additional accelerating energy as the number of inelastic collision increase, this means that if an electron inelastically collides twice with atoms their total energy gained is $$E_2=2E_a+2\delta_2$$. For n inelastic collisions, the total energy gained by an electron can be expressed as below:   $$E_n=n(E_a+\delta_n) \text{ where } \delta_n=n\frac{n}{L}E_a$$.   The two equations above can be used to derive an expression for the spacing between two minimas (refer to Appendix). Appendix A).  The expression $\Delta E(n)=[1+\frac{n}{L}(2n-1)]E_a$ shows that the spacing between two anode voltage minima is increasing. The lowest excitation level can be derived by setting n=0.5. \begin{equation}  \label{eq:lowestlevel}  E_a=\Delta E(0.5)