(a) What maximum light wavelength will excite an electron in the valence band of diamond to the conduction band? The energy gap is 5.50 eV. (b) In what part of the electromagnetic spectrum does this wavelength lie?

Short Answer

Expert verified

a) The maximum wavelength of the light that will excite electrons in the valence band of diamond to the conduction band is 226 nm.

b) The wavelength lies ultraviolet region in the electromagnetic spectrum.

Step by step solution

01

The given data

Energy gap of diamond,Eg=5.50eV

02

Understanding the concept of energy gap

The valence and the conduction band are separated by an energy gap. When the electron jumps from the conduction band to the valence band, a photon is released and the energy of the photon is equal to the energy gap between those two bands.

Formula for the wavelength of the released photon is given as-

E=hcλ

Here, c is the speed of light in vacuum, E is the energy of the photon, λ is the wavelength of photon and his the plank’s constant.

03

a) Calculation of the maximum wavelength of the light

Using the concept and the given energy gap in equation (i), we can get the value of the maximum wavelength required for the excitation as follows:

λmax=hcEg=6.626×10-34J.s3×10-8m/s5.5eV1.6×10-19J/eV=2.26×10-7m=226nm

Hence, the wavelength of the photo is 226 nm.

04

b) The wavelength region in the electromagnetic spectrum

Comparing with the electromagnetic spectrum, we can see that the wavelength λ=226nmlies in the ultraviolet region.

Hence, the region of the spectrum is ultraviolet region.

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Most popular questions from this chapter

A certain material has a molar mass of 20.0g/mol , Fermi energy of 5.00 eV , and 2 valence electrons per atom. What is the density (g/cm3)?

(a) Show that the slope dP/dEof Eq. 41-6 evaluated atE=EFis -1/4kT. (b) Show that the tangent line to the curve of Fig. 41-7bevaluated atE=EFintercepts the horizontal axis atE=EF+2kT.

In a simplified model of an undoped semiconductor, the actual distribution of energy states may be replaced by one in which there are NVstates in the valence band, all having the same energyEV, andNCstates in the conduction band all these states having the same energyEc. The number of electrons in the conduction band equals the number of holes in the valence band.

  1. Show that this last condition implies that Ncexp(Ec/kT)+1=Nvexp(Ev/kT)+1in whichEc=Ec-EF and Ev=-(Ev-EF).
  2. If the Fermi level is in the gap between the two bands and its distance from each band is large relative to kT then the exponentials dominate in the denominators. Under these conditions, show that EF=(Ec+Ev)2+kTIn(Nv+Nc)2and that ifNvNc , the Fermi level for the undoped semiconductor is close to the gap’s center.

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A certain computer chip that is about the size of a postage stamp 2.54cm×2.22cmcontains about 3.5 million transistors. If the transistors are square, what must be their maximumdimension? (Note:Devices other than transistors are also on the chip, and there must be room for the interconnections among the circuit elements. Transistors smaller than 0.7μmare now commonly and inexpensively fabricated.)

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