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(Solved): 1.3 Consider a stack of three wafers at room temperature. The top one is GaAs(Egl=1.42eV), the m ...




1.3 Consider a stack of three wafers at room temperature. The top one is \( \mathrm{GaAs}\left(E_{\mathrm{gl}}=1.42 \mathrm{e
11 Plancks radiation law gives the frequency distribution of energy radiated by an ideal black body. It is given by
\[
E(v)=
In this equation, \( h \) is Planck constant, \( k \) is Boltzmann constant, \( c \) is the speed of light in vacuum, \( T \)
1.7 This problem is about estimating the size of a hydrogen atom and the binding energy of its electron. This is an easy calc
1.3 Consider a stack of three wafers at room temperature. The top one is , the middle one is , and the bottom one is , as sketched below. To this stack, we shine three lasers with wavelengths , and , once from above and a second time from below. For each illuminating condition, in which wafer is each laser beam absorbed? Explain. 11 Planck's radiation law gives the frequency distribution of energy radiated by an ideal black body. It is given by In this equation, is Planck constant, is Boltzmann constant, is the speed of light in vacuum, is absolute temperature, and is the frequency of radiation. This equation is given in the SI system of units where has units of . Calculate the photon spectral density (photon flux per unit frequency) emitted by a blackbody at room temperature at an energy equal to the bandgap of at room temperature. 1.7 This problem is about estimating the size of a hydrogen atom and the binding energy of its electron. This is an easy calculation and the result is surprisingly accurate. This is how this can be done. Consider the electron as a classical particle that is bound to the proton by the attractive electrostatic force. The electron performs a circular orbit around the proton. The quantum mechanics are introduced by assuming that the length of the orbit is equal to the de Broglie wavelength of the electron. The solution to the problem lies in computing the total energy of the electron, the sum of its kinetic energy plus its potential energy, and finding the radius that minimizes it. Proceed as follows. (a) Using Eqs. (1.3) and (1.4), express the kinetic energy of the electron in terms of its de Broglie wavelength. Assume that the de Broglie wavelength is equal to the circumference of the orbit and derive an expression for the kinetic energy in terms of the orbital radius. (b) From elemental electrostatics, write an expression for the potential energy of the electron in terms of the radius of its orbit. Get the total energy of the electron. Find the radius that minimizes it. Derive a simple expression for the total energy of the electron in terms of fundamental parameters. (c) Put numbers to these expressions. Use the SI system. Give the final result in nanometer and electronvolt.


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