Probability that the electron will pass through the barrier?

In summary: Just a thought.In summary, the conversation discusses the probability of an electron passing through a barrier of width 0.7 nm and height 3.2 eV when it has an energy of 2.2 eV. The transmission probability is calculated using the formula T=Ge^(-2kL), where G=16(e/v)(1-e/v) and k=sqrt(2m/(h/2∏)^2(U-E). Despite multiple attempts, the correct probability of 1.0 is not obtained, but it is unclear if this is due to an error in the formulas or in the system marking the answer.
  • #1
Gee Wiz
137
0

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.)
barrier.gif


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?
 
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  • #2
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..?
 
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  • #3
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##:
$$k = \sqrt{\frac{2m_e(U-E)}{\hbar^2}} = \sqrt{\frac{2(m_ec^2)(U-E)}{(\hbar c)^2}}$$
 
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  • #4
Okay, that makes sense so for k I get 5.131. So then I took
T=3.4375e^(-2*5.131*.7)
 
  • #5
I think I am still missing something, because I keep getting .002607 at my T, yet this is not correct
 
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  • #7
How do you know it's not correct?
 
  • #8
rude man said:
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.
 
  • #9
I know it is not correct because the online homework marks it incorrectly...but maybe the system is having issues..?
 
  • #10
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.
 

Related to Probability that the electron will pass through the barrier?

1. What is the probability that an electron will pass through a barrier?

The probability of an electron passing through a barrier depends on several factors such as the energy of the electron, the height and width of the barrier, and the properties of the material making up the barrier. It can be calculated using mathematical equations such as the Schrödinger equation.

2. How does the energy of an electron affect its probability of passing through a barrier?

The higher the energy of an electron, the greater its probability of passing through a barrier. This is because higher energy electrons have shorter wavelengths, making them more likely to tunnel through the barrier. Low energy electrons have longer wavelengths and are more likely to be reflected by the barrier.

3. Can an electron pass through a barrier with 100% probability?

No, it is not possible for an electron to pass through a barrier with 100% probability. There will always be a small chance of the electron being reflected or scattered by the barrier. However, this probability can be made very close to 100% by increasing the energy of the electron or reducing the height and width of the barrier.

4. How does the thickness of a barrier affect the probability of an electron passing through it?

The thickness of a barrier does not directly affect the probability of an electron passing through it. However, thicker barriers will require higher energies for the electron to tunnel through, resulting in a lower probability. Thinner barriers will have lower energy requirements and a higher probability of electron passage.

5. What are some real-life applications of studying the probability of electron tunneling through barriers?

Studying the probability of electron tunneling through barriers has many practical applications, such as in the development of transistors and other electronic devices. It is also used in the field of quantum computing, where the manipulation of electron tunneling is crucial for creating qubits. In addition, this concept is important in understanding the behavior of electrons in materials and can be applied in the development of new materials with unique properties.

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