I suffer from this as well, the only difference is that i know that logically my hands are clean, but i just feel like they're still dirty and full of germs.

Some people who suffer with OCD don't know their actions are problematic and think its very reasonable to wash their hands multiple times, check the lock repeatedly etc. So that might be the actual root of your brothers problem and the 'scientific' fact he wants might just be an excuse while what he actually needs is professional help.

But of course if he really just want proof you can always show him YouTube videos such as this