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When I type the following formula in LaTeX

$\ce{^{4}He + \gamma \rightarrow {2}p^{+} + 2n}$

I get a very weird space between the 2 and n in the last term, but there isn't any between the second last term.

But when I added a bracket on the 2 in the last term, the horizontal space disappeared:

$\ce{^{4}He + \gamma \rightarrow {2}p^{+} + {2}n}$

Is this the proper way to eliminate the space? Or should I just leave it with the original form?

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{2} is an escape mechanism. Simply write 2.

\rightarrow should not be used. Use -> instead.

You don't need p^{+}, p+ does the trick as well.

So, in summary, write \ce{^4He + \gamma{} -> 2p+ + 2n}, this looks how the package author intended. And yes, there is a small space after stoichiometric numbers.

For details, see the documentation.

As a side note: It is correct to use \gamma here, not $\gamma$, because it is no variable that stands for a number. However, you should make sure you load a font that includes an upright gamma. Again, see the documentation.

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