Probability that the electron will pass through the barrier?

[Gee Wiz]

Homework Statement

An electron of energy E = 2.2 eV is incident on a barrier of width L = 0.7 nm and height Vo = 3.2 eV as shown in the figure below. (The figure is not drawn to scale.)

What is the probability that the electron will pass through the barrier?
The transmission probability is?

Homework Equations

T=Ge^(-2kL)
G=16(e/v)(1-e/v)
k=sqrt(2m/(h/2∏)^2(U-E)

The Attempt at a Solution

So I thought this was straight forward and was putting all the values into the formulas and I keep getting 0. Which is not correct...is there something I am overlooking?

 

[Gee Wiz]

I got G = 3.4375 eV
k= 5.125e9 J

Am I missing that T is just a coefficient and I should use it as something else..?

 

[vela]

The units you have for G are wrong, though the number is right. The units of $k$ should be 1/length, and it's way off numerically.

It's useful to memorize certain combinations of constants:
\begin{align*}
m_e c^2 &= 511000\text{ eV} \\
\hbar c &= 197\text{ eV nm}
\end{align*} where $c$ is the speed of light. Your expression for $k$ can be rewritten slightly by introducing convenient factors of $c$:
$$k = \sqrt{\frac{2m_e(U-E)}{\hbar^2}} = \sqrt{\frac{2(m_ec^2)(U-E)}{(\hbar c)^2}}$$

 

[Gee Wiz]

Okay, that makes sense so for k I get 5.131. So then I took
T=3.4375e^(-2*5.131*.7)

 

[Gee Wiz]

I think I am still missing something, because I keep getting .002607 at my T, yet this is not correct

 

[rude man]

here's a nifty site for this. Their formula is correct, I think it's the same as yours.

HOWEVER: they also have a calculator and when I inputed your parameters I get that the probability is 1.0!

I don't know if it's right or wrong, but there it is.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html

 

[vela]

How do you know it's not correct?

 

[Gee Wiz]

here's a nifty site for this. Their formula is correct, I think it's the same as yours.

HOWEVER: they also have a calculator and when I inputed your parameters I get that the probability is 1.0!

I don't know if it's right or wrong, but there it is.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html

I tried that, but unfortunately it was not correct. But thank you for the suggestion.

 

[Gee Wiz]

I know it is not correct because the online homework marks it incorrectly...but maybe the system is having issues..?

 

[vela]

Are you sure you're using the right formulas? i get the same result you do, but I just assumed you looked up the right formulas. It seems unlikely that hyperphysics would have an erroneous page up.

It could also be you're entering the answer incorrectly, e.g. sig figs, units, etc.