1. The problem statement, all variables and given/known data A stream of electrons is of energy E is incident on a potential barrier of height U and thickness d. Even though U >> E, 5% of the electrons tunnel through the barrier. If the thickness of the barrier decrease to 0.86 d, what percentage of the electrons will tunnel through? 2. Relevant equations P(d) = 0.05 = exp(-2αd) P(d*a) = exp(-2αd*a) = exp(-2αd)^a = 0.05^a Here a is a constant. Convert to %. 3. The attempt at a solution At first I tried "reasoning" my way through it (haha), thinking that if the thickness (d) decreased from an arbitrary 1 (100%) to a 0.4 (40%), then that's a 60% change in the thickness, meaning the 5% would also change by 60%, making that a 3%. But clearly...I'm missing something right in front of me. I guess what's throwing me this time is the equation offered in the hint of: P(d*a) = exp(-2αd*a) = exp(-2αd)^a = 0.05^a. Where did the "a" come from, and where do plug in numbers to convert it to said percent?