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Chapter 6: Q21E (page 1355)

An electron is bound in a square well of depthU0=6E1-1DW. What is the width of the well if its ground颅 state energy is2.00eV?

Short Answer

Expert verified

The width of the well is3.43脳10-10m, if its ground state energy is2.00eV.

Step by step solution

01

Define the energy level.

The energy levels of a particle of massmin a box widthLis:

En=P22m=n2h28mL2=n2蟺2h22mL2(n=1,2,3...)

The ground state energy as a fraction of the ground-level energy for an infinitely deep well(E1-IDW)is given by:

E1=0.625E1-1DW

02

Determine the width of the well.

Given that, the energy level of square well of depth isU0=6E1-IDWand ground state energy is2.00eV.

The ground-state energy E1:

E1=2.00脳1.60脳10-191=3.60脳10-19

The mass of electron is 9.11脳10-31and value of h=1.055脳10-34J鈰�s.

The width of the well is:

L=0.625蟺2h22mE1

=蟺1.055脳10-340.62529.11脳10-313.20脳10-19=3.43脳10-10m

Hence, the width of the well is 3.43脳10-10m, if its ground state energy is 2.00eV.

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