Question 5: (Numerical) Even the smoothest surfaces are "rough" when viewed at a scale of

100nm

. When two very smooth metal surfaces are placed in contact with each other, the actual distance between the surfaces varies from

0nm

at points of contacts to about

100nm

. Take the average distance between the two surfaces due to imperfect smoothness to be

50nm

. The work function

\\\\phi

of

Al

is

4.3eV

. What is the probability that an electron will tunnel between two pieces of

Al

in contact? Express your answer in powers of 10 , noting that

ln102.3

.