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Chapter 38: Q. 18 (page 1114)

Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 500nm?

Short Answer

Expert verified

The potential differenceΔV=6.02·10-6V

Step by step solution

01

Given information 

To find the potential difference of electron from rest to de Broglie wave length of500nm

02

Calculation 

We can start the solution with expression for de-Broglie wavelength

λ=hmvv=hmλEk=Umv22=eΔVΔV=mv22eΔV=mh22em2λ2ΔV=h22emλ2ΔV=2·1.6·10-19·9.11·10-31·500·10-922VΔV=6.02·10-6V

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Most popular questions from this chapter

a. Explain why the graphs of Figure 38.3 are mostly horizontal for ∆V > 0.

b. Explain why photoelectrons are ejected from the cathode with a range of kinetic energies, rather than all electrons having the same kinetic energy.

c. Explain the reasoning by which we claim that the stopping potential Vstop indicates the maximum kinetic energy of the electrons

Imagine that the horizontal box of Figure 38.14 is instead oriented vertically. Also imagine the box to be on a neutron star where the gravitational field is so strong that the particle in the box slows significantly, nearly stopping, before it hits the top of the box. Make a qualitative sketch of the n = 3 de Broglie standing wave of a particle in this box.

a. Calculate the de Broglie wavelength of the electron in the n=1,2,and3states of the hydrogen atom. Use the information in Table 38.2 .

b. Show numerically that the circumference of the orbit for each of these stationary states is exactly equal to n de Broglie wavelengths.

c. Sketch the de Broglie standing wave for then=3 orbit

An experiment was performed in which neutrons were shot through two slits spaced 0.10 mm apart and detected 3.5 m behind the slits. Figure P38.49 shows the detector output. Notice the 100μmscale on the figure. To one significant figure, what was the speed of the neutrons?

An electron confined in a one-dimensional box is observed, at different times, to have energies of 12 eV, 27 eV, and 48 eV. What is the length of the box?
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