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In this problem, there are no given sig figs other than the energy levels, which apparently don't count because the final answer for part (a) has 3 sig figs. How is it that the answer has three sig figs?
The question asks to calculate the wavelength and since the majority of the wavelengths on the electromagnetic radiation spectrum range from ~300nm to ~1000nm it would only make sense for the answer to be in between those two numbers and have three significant figures, but in this case, I don't think the grader would be too strict on significant figures.
I agree with the other replies, don't worry too much on the significant figures on that problem. In most cases you should go to the lowest significant figure, but in that problem I would just go with three significant figures.
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