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Chapter 40: Q. 25 (page 1175)

What is the probability that an electron will tunnel through a 0.45nmgap from a metal to a STM probe if the work function is 4.0eV?

Short Answer

Expert verified

The probability is9.5脳10-5.

Step by step solution

01

Given information 

We have given,

Work function =4eV

penetration depth =0.45nm

We have to find the probability of tunneling.

02

Simplify 

We know the penetration depth can be written as ,

畏=h2蟺2m(U0-E)

substitute the all value

畏=(6.634脳10-34J.s)2蟺2脳9.1脳10-31kg(4eV脳1.6脳10-19)畏=(6.634脳10-34J.s)2蟺脳10.79脳10-25畏=0.0972nm

and we know the probability

P=e-2w/畏P=e-2(0.45nm)/(畏=0.0972nm)P=e-0.08748P=9.5脳10-5

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Most popular questions from this chapter

The electrons in a rigid box emit photons of wavelength1484nmduring the3s2 transition.

a. What kind of photons are they鈥攊nfrared, visible, or ultraviolet?

b. How long is the box in which the electrons are confined.

| FIGURE EX40.4 shows the wave function of an electron in a rigid box. The electron energy islocalid="1650137157775" 12.0eV. What is the energy, in localid="1650137162096" eV, of the next higher state?

a. Sketch graphs of the probability density 蠄x2for the four states in the finite potential well of Figure 40.14a. Stack them vertically, similar to the Figure 40.14a graph of 蠄x.

b. What is the probability that a particle in then=2 state of the finite potential well will be found at the center of the well? Explain.

c. Is your answer to part b consistent with what you know about standing waves? Explain.

a. What is the probability that an electron will tunnel through a0.50nmair gap from a metal to a STM probe if the work function is 4.0eV?

b. The probe passes over an atom that is0.050nm鈥渢all.鈥� By what factor does the tunneling current increase?

c. If a 10%current change is reliably detectable, what is the smallest height change the STM can detect?

Sketch the n=4 wave function for the potential energy shown in FIGURE EX40.13.
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