How many peaks of HCl are found in a mass spectrum?
Collision between an electron and the molecule during a MS-experiment usually results in two phenomena: 

\begin{align}
\begin{cases}
\ce{AB + e &amp;-&gt; [AB]+ + 2e} &amp;\text{electron ionization}\\
\ce{AB + e &amp;-&gt; [AB]-} &amp;\text{resonance capture}
\end{cases}
\end{align}

Resonance capture is less frequent and usually doesn't add much to the spectra. For $\ce{HCl}$ considering electron ionization as the primary process the following process takes place:

$$\ce{HCl + e -&gt; [HCl]+ + 2e}$$

Based on ionization method (e.g. applied energy) several fragmentation processes may accompany the formation of cation/cation-radical ($\ce{[HCl]+}$/$\ce{[HCl]^{+.}}$):

\begin{align}
\ce{[HCl]+ &amp;-&gt; H+ + Cl^. }\\
\ce{[HCl]+ &amp;-&gt; H^. + Cl+ }\\
\ce{[HCl]+ + e &amp;-&gt; H+ + Cl-}
\end{align}

Fragmentation is often followed by recombination acts of different degrees of probability, e.g.:
\begin{align}
\ce{H+ + Cl- &amp;-&gt; HCl}\\
\ce{H+ + HCl &amp;-&gt; [H2Cl]+}\\
\ce{H^. + [H2Cl]+ &amp;-&gt; [H3Cl]^.+}
\end{align}

One can possibly observe peaks of $\ce{[H]+}$ and $\ce{[H2]+}$, but those are usually have negligible intensities due to recombination processes. 

Regarding the spectra OP provided, it looks somewhat strange as the base peak @ $m/z = 36$ is not $100\%$ (approx. $90\%$ instead). I would recommend to check for the experimental data in more reliable sources, e.g. in NIST database: 



Considering the fragmentation processes and the fact that $\ce{^{35}Cl} : \ce{^{37}Cl} = 3 : 1$, one can perform the following peak assignment:

\begin{array}{rrr}
m/z &amp; \text{r.i.}, \% &amp; \text{fragment}\\
\hline
35 &amp; 18  &amp; \ce{[^{35}Cl]+}\\
36 &amp; 100 &amp; \ce{[^1H^{35}Cl]+}\\
37 &amp; 6   &amp; \ce{[^{37}Cl]+}\\
38 &amp; 33  &amp; \ce{[^1H^{37}Cl]+}\\
\hline
\end{array}

Alternatively, for $m/z = 37$ and $m/z = 38$ fragments $\ce{[^1H2^{35}Cl]+}$ and $\ce{[^1H3^{35}Cl]+}$, respectively, could be proposed, but it wouldn't be correct due to the following:


recombination acts leading to the formation of large molecules as detected end-products are less possible and usually result in much smaller peaks;
observed relative intensities are not in agreement with isotope distribution for chlorine ($\ce{^{35}Cl} : \ce{^{37}Cl} = 3 : 1$, which is in agreement with r.i. ratios for $\ce{[^{35}Cl]+} : \ce{[^{37}Cl]+} = 18 : 6$ and $\ce{[^1H^{35}Cl]+} : \ce{[^1H^{37}Cl]+} = 100 : 33$, but not with alternatively proposed fragments);
the problem itself states that 


  hydrogen chloride molecules will split into atoms.