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Chapter 39: Q5P (page 1215)

What must be the width of a one-dimensional infinite potential well if an electron trapped in it in the n=3 state is to have an energy of 4.7 eV ?

Short Answer

Expert verified

0.85 nm

Step by step solution

01

Given data

En=4.7eVn=3

02

Energy in a potential well

The nth state energy of a particle of mass m in an infinite potential well of width L is

En=n2h28mL2........1

03

Determining the width of the potential well

Here h is the Planck's constant having value

h=6.626脳10-34J.sandc=2.998脳108m/s,hc=6.626脳10-34J.s2.998脳108m/s1.602脳10-19J/eV10-9m/nm=1240eV.nm

Using the mc2value for an electron from Table 37-3 511脳103eV, Eq.39 鈥� 4 can be rewritten as

En=n2h28mL2=n2hc28mc2L2

For n=3,

L=nhc8mc2En=31240eV.nm8511脳103eV4.7eV=0.85nm

Thus, the width is 0.85nm.

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Most popular questions from this chapter

An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to the energy of the n = 5 level? (c) Show that no pair of adjacent levels has an energy difference equal to the energy of the n = 6 level.

A cubical box of widths Lx=Ly=Lz=Lcontains an electron. What multiple of ,h2/8mL2where, m is the electron mass, is (a) the energy of the electron鈥檚 ground state, (b) the energy of its second excited state, and (c) the difference between the energies of its second and third excited states? How many degenerate states have the energy of (d) the first excited state and (e) the fifth excited state?

What is the ratio of the shortest wavelength of the Balmer series to the shortest wavelength of the Lyman series?

The two-dimensional, infinite corral of Fig. 39-31 is square, with edge length L = 150 pm. A square probe is centered at xy coordinates (0.200L,0.800L)and has an x width of 5.00 pm and a y width of 5.00 pm . What is the probability of detection if the electron is in the E1.3energy state?

(a) Show that the terms in Schr枚dinger鈥檚 equation (Eq. 39-18) have the same dimensions. (b) What is the common SI unit for each of these terms?
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