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Chapter 40: Q. 10 (page 1175)

The energy of an electron in a 2.00eVdeep potential well is 1.50eV. At what distance into the classically forbidden region has the amplitude of the wave function decreased to 25% of its value at the edge of the potential well?

Short Answer

Expert verified

The distance is3.88脳10-10m.

Step by step solution

01

Given information 

We have given,

Energy of the electron =2eV

Height of the potential =1.5eV

We have to find the distance where the amplitude will decreases to25%.

02

Simplify

We know the potential depth is given by,

H=h2蟺2m(V0-E)H=6.63脳10-34J.s2蟺2脳9.1脳10-31kg(2eV-1.5eV)脳1.6脳10-19JH=2.8A0

The forbidden can be found as

蠁=蠁edgese-(x-L)/H(x-L)=Hln蠁edge蠁(X-L)=(2.8脳10-10m)ln(10.25)(x-L)=(2.8脳10-10m)(1.386)(x-L)=3.88A0

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