Tunneling at potential step

In summary, the conversation discusses a problem involving a beam of particles of energy 9 eV and a step potential. The equation given is used to calculate the height of the step potential, but it may be difficult to remember and solve without a calculator or equation sheet. The correct answer is 8 eV, which can be estimated by considering the significant reflection for 5 eV. There may be a sign error in the formula given.
  • #1
Helmholtz
19
0

Homework Statement



A beam of particles of energy E = 9 eV strikes on a step potential and 25% of the beam's particles is reflected back. What is the height of the step potential?

(A) 4 eV
(B) 8 eV
(C) 3 eV
(D) 1 eV
(E) 5 eV

Homework Equations



√(R) = [√(E)-√(E-U)]/[√(E)-√(E_U)]

The Attempt at a Solution



Just plug and chug the equation I have, but this is for a timed test without a calculator or equation sheet. This seems clunky to remember, solve and do in such conditions. Is there a simpler way? I get 8eV, which is the correct answer.
 
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  • #2
You can remember that you need a significant potential step to get significant reflection.
Estimate reflection for 5 eV, if the value is too low, it has to be 8 eV.

Is there a sign error in your formula?
 

What is tunneling at potential step?

Tunneling at potential step is a quantum mechanical phenomenon in which a particle, such as an electron, can pass through a potential barrier even though it does not have enough energy to overcome the barrier classically. This is possible due to the wave-like nature of particles, which allows them to exist in a probabilistic state on both sides of the barrier.

What is the significance of tunneling at potential step?

Tunneling at potential step plays a crucial role in many areas of science, including physics, chemistry, and engineering. It is important in understanding the behavior of particles in quantum systems, and has practical applications such as in quantum computing and tunnel diode technology.

How does tunneling at potential step occur?

Tunneling at potential step occurs when a particle encounters a potential barrier that is higher than its energy level. In classical physics, the particle would be unable to pass through the barrier. However, in quantum mechanics, the particle is described by a wave function that extends beyond the barrier, allowing for a small probability of the particle to tunnel through the barrier.

What factors affect the probability of tunneling at potential step?

The probability of tunneling at potential step is affected by several factors, including the energy level of the particle, the width and height of the potential barrier, and the mass of the particle. Higher energy levels, narrower and lower barriers, and lighter particles all increase the probability of tunneling occurring.

How is tunneling at potential step observed and measured?

Tunneling at potential step can be observed and measured through various experimental techniques, such as scanning tunneling microscopy and tunneling spectroscopy. These methods involve sending a current or voltage through a thin barrier and measuring the resulting tunneling current, which can provide information about the properties of the barrier and the particles involved.

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