Question

An electron is travelling down a long wire, when it encounters a small gap. The probability of the eletron tunneling through this gap is 1/10,000. What will be the probability of tunneling through if:

(a)The width of the gap were to be decreased by a factor of 2?

(b) A different metal is used in the wire, one whose work function is twice that of the original wire?

(c) The experiment was set up in a different universe, where his ten times bigger than it is in our universe?

Answer 1

Tunneling probability is given by following expression

P« exp(-21 V2m(V - E)

Where L is length of gap

m is mass of electron

V is energy barrier strength

h is planck's constant

E is energy of electron

(a) therefore if we decrease gap width by a factor of 2, probability will become square root of the earlier probability.

Square root of (1/10,000) = 1/100

Therefore probability will become 1/100 = 0.01

(b) if work function becomes twice than probability becomes
ZA(00001/1)
= 2.2 x $10^{-6}$

(c) if h becomes 10 times then probability will become

(1/10000)=(1/10)
= 0.398 $\cong$ 0.4