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Rorshach
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Here is one problem I have, I think it is simple, but then again I thought that every problem I had was like that only to discover that there was some trick in the middle, so please help.
Caesium has exit work Wut = 1.9 eV. This means, therefore, that there are electrons in the cesium such that it is enough to give such an electron the extra energy 1.9 eV to make it free so that it can leave the surface. If two pieces of cesium are very near each other, such an electron can tunnel from one piece to the other and vice versa. What should the distance between the pieces be if the probability of tunneling will be 1%?
Line 1: use the approximate expression for the tunnelling.
Line 2: the electron has a specific energy E in the material. If so, what corresponds to the term V0 − E in this context?
[tex]D=T*(Tconjugate)=\frac{4λ2μ2}{((λ2+μ2)2*sinh2(λa+4λ2μ2))}[/tex]
[tex]λ=\frac{\sqrt{2m(U-E)}}{\hbar}[/tex]
[tex]μ=\frac{\sqrt{2mE}}{\hbar}[/tex]
I tried to approach this as a problem of a finite potential barrier with three schrodinger equations, that would give the equation for transmission probability. They ask for approximated expression, so I think it is:
[tex]D=16*\frac{E}{u}*(1-\frac{E}{u})*exp(-2λa)[/tex]
and a is the distance I am looking for.
Caesium has exit work Wut = 1.9 eV. This means, therefore, that there are electrons in the cesium such that it is enough to give such an electron the extra energy 1.9 eV to make it free so that it can leave the surface. If two pieces of cesium are very near each other, such an electron can tunnel from one piece to the other and vice versa. What should the distance between the pieces be if the probability of tunneling will be 1%?
Line 1: use the approximate expression for the tunnelling.
Line 2: the electron has a specific energy E in the material. If so, what corresponds to the term V0 − E in this context?
Homework Equations
[tex]D=T*(Tconjugate)=\frac{4λ2μ2}{((λ2+μ2)2*sinh2(λa+4λ2μ2))}[/tex]
[tex]λ=\frac{\sqrt{2m(U-E)}}{\hbar}[/tex]
[tex]μ=\frac{\sqrt{2mE}}{\hbar}[/tex]
The Attempt at a Solution
I tried to approach this as a problem of a finite potential barrier with three schrodinger equations, that would give the equation for transmission probability. They ask for approximated expression, so I think it is:
[tex]D=16*\frac{E}{u}*(1-\frac{E}{u})*exp(-2λa)[/tex]
and a is the distance I am looking for.
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