typos fixed thanks to Dean

1 files changed, 11 insertions, 8 deletions

diff --git a/spectr.tex b/spectr.tex
index 0b19b8b..98d518c 100644
--- a/spectr.tex
+++ b/spectr.tex
@@ -140,7 +140,7 @@ energies).
 
 
 To take into account the modification of the atomic spectra while still using the same basic
-equations as for the hydrogen, it is convenient to introduce a small correction $\Delta_l$ to the
+equations used for hydrogen, it is convenient to introduce a small correction $\Delta_l$ to the
 principle quantum number $n$ to take into account the level shifts. This correction is often called a
 {\it quantum defect}, and its value % an effective nuclei charge $Z^*$ keeping the For each particular value
 %of angular momentum $l$ the energy spectrum follows the same scaling as hydrogen atom, but with an
@@ -160,7 +160,7 @@ those with initial electron states of $d$-orbital ( $l=2$) always appeared \text
 spectral lines of \textbf{P}rinciple  series (initial state is $p$-orbital, $l=1$) reproduced the
 hydrogen spectrum most accurately (even though at shifted frequencies), while the
 \textbf{F}undamental (initial electron state is $f$-orbital, $l=3$) series matched the absolute
-energies of the hydrogen most precisely. The orbitals with higher value of the angular momentum are
+energies of the hydrogen most precisely. The orbitals with higher values of the angular momentum are
 denoted in an alphabetic order ($g$, $h$, \textit{etc}.) }:
 \begin{equation}\label{qdef}
 E_{nl}=-\frac{hc{R_y}}{(n-\Delta_l)^2}%=-\frac{hc{R_y}}{(n-\Delta_l)^2}
@@ -217,7 +217,8 @@ According to that rule, only transitions between two ``adjacent'' series are pos
 forbidden. The strongest allowed optical transitions are shown in Fig. \ref{natrns}.
 \begin{figure}
 \includegraphics[height=\columnwidth]{./pdf_figs/natrans}
-\caption{\label{natrns}Transitions for Na. The wavelengths of selected transition are shown in {\AA}.
+\caption{\label{natrns}Transitions for Na. The wavelengths of selected
+	transitions are shown in {\AA}.
 Note that $p$ state is now shown in two columns, one referred to as $P_{1/2}$ and the other as
 $P_{3/2}$. The small difference between their energy levels is the ``fine structure''.}
 \end{figure}
@@ -231,7 +232,7 @@ angular momentum. Proper treatment of spin requires knowledge of quantum electro
 the Dirac equation; for now spin can be treated as an additional quantum number associated with any
 particle. The spin of electron is $1/2$, and it may be oriented either along or against the non-zero
 electron's angular momentum. Because of the weak coupling between the angular momentum and spin,
-these two possible orientation results in small difference in energy for corresponding electron
+these two possible orientations result in small differences in energy for corresponding electron
 states.
 
 \section*{Experimental setup}
@@ -270,7 +271,8 @@ should align the position of the telescope tube again (with the help of the inst
 that has 600 lines per mm. A brief summary of diffraction grating operation is given in the Appendix
 of this manual. If the grating is not already in place, put it back on the baseclamp and fix it
 there. The table plate that holds the grating can be rotated, so try to orient the grating surface to
-be maximally perpendicular to the collimator axis. However, the accurate measurement of angle does
+be maximally perpendicular to the collimator axis. However, the accurate
+measurement of angles does
 not require the perfect grating alignment. Instead, for each spectral line in each diffraction order
 you will be measuring the angles on the left ($\theta_l$) and on the right ($\theta_r$), and use both
 of the measurements to figure out the optical wavelength using the following equation:
@@ -369,7 +371,7 @@ states principle numbers ($n_1$ and $n_2$) for each line using Fig.~\ref{Hspec.f
 
 Make a plot of $1/\lambda$  vs $1/n_1^2$ where $n_1$ = the principal quantum number of the electron's
 initial state. Put all $\lambda$ values you measure above on this plot.
-Your data point should form a
+Your data points should form a
 straight line. From Equation~(\ref{Hlines_inf}) determine the physical meaning of both slope and
 intercept, and compare the data from the fit to the expected values for each of them. The slope
 should be the Rydberg constant for hydrogen, ${R_y}$. The intercept is ${R_y}/(n_2)^2$. From this,
@@ -383,8 +385,9 @@ the measurements.
 
 Double check that you see a sharp spectrum in the spectrometer (adjust the width of the collimator
 slit if necessary). In the beginning it will be very useful for each lab partner to quickly scan the
-spectrometer telescope through all first-order lines, and then discuss which line you see corresponds
-to with transition in Table~\ref{tab:sodium} and Fig.~\ref{natrns}. Keep in mind that the color
+spectrometer telescope through all first-order lines, and then discuss
+which lines you see correspond
+with  which transitions in Table~\ref{tab:sodium} and Fig.~\ref{natrns}. Keep in mind that the color
 names are symbolic rather than descriptive!
 
 After that, carefully measure the left and right angles for as many