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Chapter 31: Q26 CQ (page 1148)

A physics student caught breaking conservation laws is imprisoned. She leans against the cell wall hoping to tunnel out quantum mechanically. Explain why her chances are negligible. (This is so in any classical situation.)

Short Answer

Expert verified

Students are unable to penetrate the prison wall because the mass is greater and the wavelength is smaller.

Step by step solution

01

Definition of DE Broglie wavelength

Matter waves, which are an example of wave鈥損article duality, are an important part of quantum mechanics theory. All matter behaves in a wave-like manner. A beam of electrons, for example, can be diffracted in the same way that a light beam or a water wave can.

02

Explanation

We know that depending on its wavelength, an object can exhibit wave, particle, or both characteristics. In the tunnelling effect, a particle with some energy penetrates a potential barrier that is higher than the energy required for the particle to jump over the barrier.

The formula also gives the DeBroglie wavelength:

\(\lambda = \frac{h}{p}\)

Because mass is inversely proportional to wavelength, we can say that the debroglie wavelength of a macroscopic particle is much smaller than that of an electron or a proton. The student in this case is a macroscopic system with a greater mass than an electron, for example. As a result, students are unable to break through the prison wall.

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