Transmission coefficient in a barrier penetration.

In summary, the conversation discusses the calculation of the transmission coefficient for an electron with total energy E=4.46 eV approaching a rectangular energy barrier with U=5.02 eV and L=949 pm. After using the equations T=e-2GL and G=\sqrt{\frac{2m(U-E)}{H}}, it was found that T=7.18E-4, but further discussion revealed that there may have been errors in accounting for the units. Upon correcting these errors, the final value for T was found to be different.
  • #1
simon8502
2
0
An electron having total energy E=4.46 eV approaches a rectangular energy barrier with U=5.02 eV and L=949 pm. Calculate this probability, which is the transmission coefficient.


I thought this would be an easy one, given that
T=e-2GL
and
G=[tex]\sqrt{\frac{2m(U-E)}{H}}[/tex] where H is the reduced Planck's constant

I just plugged in the numbers,
U=5.02eV
E=4.46eV
L=949E-12m
m=9.109E-31kg

I found that T=7.18E-4, which is apparently wrong. Can anyone point out where I went wrong?


PS. oops I just realized that I should've put this in the homework help section. First time posting. Sorry!
 
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  • #2
Did you account for the units? Your energies are in eV, while your mass and length are in SI units. There are some factors to take into account so that the quantity [tex]GL[/tex] is properly dimensionless.
 
  • #3
Found that that the hbar value I used was wrong by a few decimals. Thanks for the help :)
 

FAQ: Transmission coefficient in a barrier penetration.

1. What is the transmission coefficient in barrier penetration?

The transmission coefficient in barrier penetration is a measure of the likelihood that a particle, such as an electron, will pass through a potential barrier. It is influenced by the energy of the particle, the height and width of the barrier, and the properties of the material the barrier is made of.

2. How is the transmission coefficient calculated?

The transmission coefficient can be calculated using the Schrödinger equation, which describes the behavior of quantum particles. It takes into account the energy of the particle, the potential barrier, and the wave function of the particle.

3. What is the significance of the transmission coefficient in barrier penetration?

The transmission coefficient is important in understanding the behavior of quantum particles in materials and devices. It helps predict the likelihood of a particle passing through a barrier and can be used to design and optimize electronic devices, such as transistors and diodes.

4. Can the transmission coefficient be greater than 1?

No, the transmission coefficient cannot be greater than 1. This would imply that the particle has a higher chance of passing through the barrier than not. The transmission coefficient is a probability and therefore must be between 0 and 1.

5. How does the transmission coefficient change with different barrier heights and widths?

The transmission coefficient is directly influenced by the height and width of the barrier. As the barrier height increases, the transmission coefficient decreases, meaning there is a lower chance of a particle passing through. Similarly, as the barrier width increases, the transmission coefficient also decreases.

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