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Chapter 40: Q. 45 (page 1177)

A proton鈥檚 energy is 1.0MeV below the top of a 10fm-wide energy barrier. What is the probability that the proton will tunnel through the barrier?

Short Answer

Expert verified

The probability that the proton will tunnel through the barrier is1.22%.

Step by step solution

01

Given Information 

We need to find the probability that the proton will tunnel through the barrier.

02

Simplify

Finding the penetration distance of the proton into the forbidden region:

畏=魔2mU0鈭�E

but we given that the proton's energy is 1.0MeVbelow the top of the well, which represents the value of U0鈭�E. Then, U0鈭�E=1MeV.

Since:

畏=1.05脳10鈭�34J鈰�s21.67脳10鈭�27kg1脳106eV脳1.6脳10鈭�19J/eV畏=4.54脳10鈭�15m=4.54fm

the probability that the proton will tunnel through the barrier is given as:

Ptunnel=e鈭�2w/畏

There, wthe width of the barrier.

Therefore:

Ptunnel=exp鈭�20fm4.54fm=0.0122=1.22%

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