Tunneling equation have all the pieces, just can't figure out the calculation

[j2dabizo]

Tunneling equation...have all the pieces, just can't figure out the calculation!

Hi,
I have an example from my book on Tunneling. All the parts of the equation are given, including the answer...put I keep coming up with the inccorect answer.

Maybe someone can clarify how to calculate the correct answer?

Here is the equation given:

T=[ 1 + (V₀² sinh²(kL)) / 4E(V₀-E)]^-1

Hope that is readable..sorry, I tried to paste and copy the equation from a bunch of sites and it just wouldn't copy. If anyone can paste the equation that would be helpful, thanks.

Given V₀= 10eV
h= plank constant (4.1359E-15 ev*s)
kL= 9.2
E= 5eV

so...the book states:

T= [1+ (10eV)² sinh²(9.2) / 4(5eV)(5eV)]^-1
= 4.1 x 10^-8

How did they get this answer...everytime i do i I get an answer of 100!

Help please. thanks.

 

[SpectraCat]

Hi,
I have an example from my book on Tunneling. All the parts of the equation are given, including the answer...put I keep coming up with the inccorect answer.

Maybe someone can clarify how to calculate the correct answer?

Here is the equation given:

T=[ 1 + (V₀² sinh²(kL)) / 4E(V₀-E)]^-1

Hope that is readable..sorry, I tried to paste and copy the equation from a bunch of sites and it just wouldn't copy. If anyone can paste the equation that would be helpful, thanks.

Given V₀= 10eV
h= plank constant (4.1359E-15 ev*s)
kL= 9.2
E= 5eV

so...the book states:

T= [1+ (10eV)² sinh²(9.2) / 4(5eV)(5eV)]^-1
= 4.1 x 10^-8

How did they get this answer...everytime i do i I get an answer of 100!

Help please. thanks.

There shouldn't be any need to use Planck's constant in that equation ... perhaps you are not aware that sinh is a single mathematical function called the hyperbolic sine (see http://en.wikipedia.org/wiki/Hyperbolic_function)? It should be available on your calculator, but if not, you can use the following identity to calculate it:

$$2sinh(x)=e^x - e^{-x}$$

Hope that helps.

Hope that helps.

 

[j2dabizo]

There shouldn't be any need to use Planck's constant in that equation ... perhaps you are not aware that sinh is a single mathematical function called the hyperbolic sine (see http://en.wikipedia.org/wiki/Hyperbolic_function)? It should be available on your calculator, but if not, you can use the following identity to calculate it:

$$2sinh(x)=e^x - e^{-x}$$

Hope that helps.

Hope that helps.

this was my issue..thanks! Too many constants! lol