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@AdamM
And the question was answered in the first response way up there ^^^ but I'll try and spell it out for you.
A 1/8" sprocket (it's a measurement, not just a fascinating number) is wider than the space between the inner plates on your 3/32" chain. So no, the two are not compatible (1/8 is 4/32, which is bigger than 3/32, see?).
If you had a 1/8" chain then it would fit on a 3/32" sprocket as the chain is wider than the sprocket teeth.
In both cases, the 'length' of the chain is the same, it, the rollers are the same distance apart along the chain length, but the width of the chain and the width of the sprocket is what's changing.
Either buy a new sprocket or a new chain.