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Chapter 6: Q15E (page 224)

Calculate the reflection probability 5evfor an electron encountering a step in which the potential drop by 2ev

Short Answer

Expert verified

The reflection probability is 0.007

Step by step solution

01

Definition of Reflection Probability

Reflection probability or reflection coefficient is defined as the ratio of amplitude of reflected wave to that of incident wave.

R=k2-k1k2+k12

Where, localid="1657549250276" k2=2m(E-v0)2 andk1=2mE2

02

Given/known parameters

E=5eV andV0=2eV

03

Solution

Substituting the values in the formula:

R=5-(-2)-55-(-2)+52

R=0.007

04

Explanation and Conclusion

The reflection probability is 0.007,i.e., there is0.7% chance of particle being reflected back.

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Most popular questions from this chapter

The diagram below plots ω(k) versus wave number for a particular phenomenon. How do the phase and group velocities compare, and do the answer depend on the central value of k under consideration? Explain.

Show that ψ(x)=A'eikx+B'e-ikxis equivalent to ψ(x)=Asinkx+Bcoskx, provided that A'=12(B-iA)B'=12(B+iA).

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To obtain a rough estimate of the mean time required for uranium-238 to alpha-decay, let us approximate the combined electrostatic and strong nuclear potential energies by rectangular potential barrier half as high as the actual 35 Mev maximum potential energy. Alpha particles (mass 4 u) of 4.3 Mev kinetic energy are incident. Let us also assume that the barrier extends from the radius of nucleus, 7.4 fm to the point where the electrostatic potential drops to 4.3 Mev (i.e., the classically forbidden region). Because Uα(1/r), this point is 35/4.3 times the radius of the nucleus, the point at which U(r) is 35 Mev. (a) Use these crude approximations, the method suggested in Section 6.3, and the wide-barrier approximation to obtain a value for the time it takes to decay. (b) To gain some appreciation of the difficulties in a theoretical prediction, work the exercise “backward” Rather than assuming a value for U0, use the known value of the mean time to decay for uranium-238 and infer the corresponding value of U0, Retain all other assumptions. (c) Comment on the sensitivity of the decay time to the height of the potential barrier.

In the E>Uopotential barrier, there should be no reflection when the incident wave is at one of the transmission resonances. Prove this by assuming that a beam of particles is incident at the first transmission resonance, E=Uo+(π2h2/2mL2), and combining continuity equations to show thatB=0. (Note: k’ is particularly simple in this special case, which should streamline your work.)
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