Roughly in order of increasing difficulty.
Uranium fission bomb, big. You got all the uranium you need and the thing can be as big as you need to to make it easier to design and build. Doesn’t have to be particulary efficient either.
Uranium fission bomb, medium. But not a bunch of uranium to use and it needs to be small enough to be pratical to use.
Uranium fission bomb, small. Roughly comparable in size and efficiency to what the miltary eventually developed.
Same sequence for Plutonium fission bomb.
Hydrogen bomb, big and crude. “Fired off” by big Uranium fission bomb. Take the fission bomb, surround it with a bunch of hydrogen, maybe use some tricks to increase the yield, but its very big and not remotely efficient.
Same deal, but using medium Uranium fission bomb.
Again, but now with small Uranium fission bomb.
Repeat Big and Crude Hydrogen bomb but now with big, medium, and small Plutonium fission bombs.
Repeat those sequences again, but now its a half ass designed hydrogen bomb that is maybe transportable by large truck or boat. Not efficient either, but signifcantly increased yield over the fission component.
Well designed hydrogen bomb. Smaller, but still pretty damn big. Big enough bang that it can be respectably called a hydrogen bomb rather than a souped up fission bomb.
Very well designed hydrogen bomb. Small enough to drop from reasonable sized planes. Also, now not some much a hydrogen bomb, but a fission fusion fission where the fusion is causing additional fission of the fissile material making it much more effiecient.
A VERY well designed hydrogen bomb. Very small, very efficient. very reliable, and a predictable yield level.
Also, how long does this prof have? A few years of full time work, or a weekend sitting around the fire at the ski lodge with a pad of paper?
I think your prof, even with a good bit of time, is going to crap out at the medium Uranium fission bomb level and the medium plutonium bomb might be a stretch.
OTOH, I think BS level physics majors might be able to pull off the big crude Uranium fission bomb.
Once the prof has his medium fission bomb, my WAG is the half ass designed hydrogen bomb is where his skill level will crap out. And the result will probably be something like "well the fission yield is gonna be about 50 kilotons. With a little “luck” we might eek out a megaton from the secondary fusion effects. Or we might have bad “luck” or missed a detail or two and just got a 100 kiloton or so extra for all our effort.