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Chapter 6: Q21DQ (page 1353)

Qualitatively, how would you expect the probability for a particle to tunnel through a potential barrier to depend on the height of the barrier? Explain.

Short Answer

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Step by step solution

01

  Tunneling probability of particle in infinite deep potential well

In case of infinite deep potential well the probability density function is completely confined in potential well which means the tunnelling probability of must be zero.

Tunneling probability of a particle in potential well of zero height

In case of potential well of zero height the tunnelling probability of a particle is must be one.

02

Conclusion  

As the tunnelling probabilities of a particle for two extreme cases are one and zero .Therefore by continuity tunnelling probability of particle any other case must lie between zero and one.

Hence higher the height of potential lower the tunnelling probability of particle.

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