I really enjoyed this, but you need a beta to clean up things that you're not seeing while you write, as is normal for all authors. I recommend tossing the chapter into google docs and using the suggestion function. Here are some quick fixes:
Nearby researchers attempt to peak before getting a headache.
Should be 'peek', peaks are mountain tops. Also 'attempted', story is past tense.
You switch between 3rd and 2nd person here. Stories have to pick one or the other and keep to it throughout.
every known material and element known to the galaxy
Double 'known', should be something like 'every material and element known to the galaxy'.
You had got to immediate work creating
Should be 'You got to'. Had is extraneous here.
and a easily synthesized a brand new element
If the following word starts with a vowel sound you need to use 'an', rather than 'a'. Should be 'and an easily synthesized'.
Everyone was starting to developed and deploy power armored soldiers and were now beginning to work on better ships, vehicles, weapons, shields.
Should be 'to develop'. Sentence structure is a little awkward.
You knew that people would either demand that you sell it to them to use for war.
Looks like a sentence that got changed halfway through. I suggest 'You knew that people would demand that you sell it to them for use in war.'
Awkward. I suggest something like 'It did not make for a pleasant mental image.'
For the largest of cities willing to convert entirely to Arc Reactors it would only take a few hundred reactors to power them, cutting down their energy costs to pretty much nothing compared to all other forms of energy generation even with constantly spending on replacement reactors and that is not even going into your industrial models.
Run on sentence, and a bit awkward at points. I suggest: 'Even the largest of cities would require only a few hundred reactors to meet all their power needs.'
It took much reassurances
Should be something like 'It took many reassurances'.
By the end of the night and a few games of biotic ball and Jack was snoring away
Extraneous 'and' and awkward phrasing. Should be 'Jack was snoring away at the end of the night after a few games of biotic ball'
Should be 'with an equally smug'.
Jack now part of the family.
Missing a word. Should be 'Jack is now part of the family'.