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Question

An electron is contained in the rectangular box of figure, with widths Lx=800 pm,Lx=1600 pm, and Lz=390 pm. What is the electron's ground state energy?

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Solution

We can the mc2 value for an electron from Table and hc=1350 eV.nm by writing as
Enx,ny,nz=2h28m(n2xL2x+n2yL2y+n2zL2z)=(hc)28(mc)2(n2xL2x+n2yL2y+n2zL2z)
For nx=ny=nz=1, we obtain
E1,1=(1240 ev.nm)8(611×103eV)(1(0.800 nm)2+1(1.600 nm)2+1(0.390 nm)2)=3.21 eV.

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