Quantum Tunneling: Estimating Probability

In summary, the conversation discusses calculating the probability of an electron tunneling through a potential barrier of certain height and width. The formula used is T=16(E/V)(1-(E/V))exp(-2\alphaa), where E and V represent the energy and potential of the electron, respectively, and \alpha is a constant calculated using the mass of the electron, Planck's constant, and the barrier height and width. The correct answer is supposed to be either 9.2x10^-9 or 4.95x10^-13, and a possible error in the calculations may be using h instead of hbar.
  • #1
fredrick08
376
0

Homework Statement


A 10eV electron is incident on a potential barrier of height 25eV and width 1nm. Estimate (order of magnitude) the probability that the electron will tunnel through the barrier, repeat your calculations for a barrier of 01.nm

Homework Equations


T=16(E/V)(1-(E/V))exp(-2[tex]\alpha[/tex]a)
[tex]\alpha[/tex]=[tex]\sqrt{}(2m(V-E))[/tex]/[tex]\hbar[/tex]

The Attempt at a Solution


E=10eV=1.6x10^-18J, V=25eV=4x10^-18J

[tex]\alpha[/tex]=[tex]\sqrt{}(2*9.1x10^-31(4x10^-18-1.6x10^-18))[/tex]/6.62x10^-34=3.157x10^9

T=3.84exp(-2*3.157x10^9*1x10^-9)=7x10^-3?

the answer is meant to be 9.2x10^-9 or 4.95x10^-13? sorry, my book says 4.95 and the lecturers notes say 9.2... doesn't matter, coz I am way way off...

please can someone help me where i am going wrong?
 
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  • #2
sorry about the latex the x is multiply
 
  • #3
please anyone?
 
  • #4
Well, the only thing I see is that instead of hbar you used h in your calculations. hbar is a factor of 2pi smaller than h.
 
  • #5
omg oops, thanks
 
  • #6
still have wrong answer, anyone know y?
 

Related to Quantum Tunneling: Estimating Probability

1. What is quantum tunneling?

Quantum tunneling is a phenomenon in which a particle can pass through a potential barrier even though it does not have enough energy to overcome it based on classical physics laws.

2. How does quantum tunneling work?

Quantum tunneling occurs due to the wave-like nature of particles at the quantum level. The particle has a probability of existing on the other side of the barrier, and this probability decreases as the barrier becomes higher or wider.

3. What is the significance of quantum tunneling in physics?

Quantum tunneling is significant in physics because it challenges the classical notion of particles being confined to a specific region. It also has practical applications in fields such as electronics, where it is used in devices like flash memory and scanning tunneling microscopes.

4. How is the probability of quantum tunneling estimated?

The probability of quantum tunneling is estimated using mathematical equations such as the Schrödinger equation and the Wentzel-Kramers-Brillouin (WKB) approximation. These equations take into account the energy of the particle, the shape and height of the barrier, and other factors to calculate the probability of tunneling.

5. What are some real-world examples of quantum tunneling?

Some real-world examples of quantum tunneling include radioactive decay, where particles tunnel out of the nucleus of an atom, and scanning tunneling microscopy, where electrons tunnel between a probe and a surface to create an image. It also plays a role in the operation of tunnel diodes and flash memory devices.

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