typos fixed thanks to Kevin

1 files changed, 8 insertions, 5 deletions

diff --git a/spectr.tex b/spectr.tex
index 4b9ad6a..0b19b8b 100644
--- a/spectr.tex
+++ b/spectr.tex
@@ -10,7 +10,7 @@
     The observation of discrete lines in the emission spectra of
     atomic gases gives insight into the quantum nature of
     atoms. Classical electrodynamics cannot explain the existence
-    of these discrete lines, whose energy (or wavelengths) are
+    of these discrete lines, whose energies (or wavelengths) are
     given by characteristic values for specific atoms. These
     emission lines are so fundamental that they are used to
     identify atomic elements in objects, such as in identifying
@@ -81,7 +81,8 @@ state $n_2$ as follows:
 
 Fig.~\ref{Hspec.fig} shows the energy levels of hydrogen, and indicates a large number of observed
 transitions, grouped into series with the common electron final state.  Emitted photon frequencies
-span the spectrum from the UV (UltraViolet) to the IR (InfraRed). Among all the series only the
+span the spectrum from the UV (UltraViolet) to the IR (InfraRed). Among all
+the series, only the
 Balmer series, corresponding to $n_2$ = 2, has its transitions in the visible part of the spectrum.
 Moreover, from all the possible transitions, we will be able to observe and measure only the
 following four lines: $n_1=6 \rightarrow  2$, $5 \rightarrow  2$, $4 \rightarrow 2$,
@@ -123,12 +124,14 @@ that the $3s$ valence
 electron experiences the electric field potential similar to that of a hydrogen atom, given by the
 Eq.~\ref{Hlevels_inf}.
 
-However, there is an important variation of the energy spectrum of alkali metals, related to the
+However, there is an important variation of the energy spectrum of alkali
+metals, which is related to the
 electron angular momentum $l$. In hydrogen the energy levels with same principle quantum number $n$
 but different electron angular momentum $l=0, 1, \cdots (n-1)$ are degenerate. For Na and others the
 levels with different values of $l$ are shifted with respect to each other. This is mainly due to the
 interaction of the unpaired electrons with the electrons of the closed shells.  For example, the
-orbits of the  electron with large angular momentum value $l$ is far above closed shell, and thus
+orbits of the  electron with large angular momentum values $l$ are far
+above the  closed shell, and thus
 their energies are basically the same as for the hydrogen atom. An electron with smaller $l$ spends
 more time closer to the nucleus, and ``feels'' stronger bounding electrostatic potential. As a result
 the corresponding energy levels are pulled down compared to those of hydrogen, and the states with the
@@ -215,7 +218,7 @@ forbidden. The strongest allowed optical transitions are shown in Fig. \ref{natr
 \begin{figure}
 \includegraphics[height=\columnwidth]{./pdf_figs/natrans}
 \caption{\label{natrns}Transitions for Na. The wavelengths of selected transition 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
+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}
 %\begin{figure}