Respuesta :
Answer:
Explanation:
The reflection coefficient is the ratio of reflected flux to the incident flux
The reflection coefficient of a srep potential when a particle is [tex]E(> U(x))[/tex] is incident on the barrier is given as:
[tex]R=(\frac{K_{1}-K_{2}}{K_{1}+K_{2}} )^2[/tex]
Where [tex]k_{1}[/tex] is the propagation constant of the incident wave and [tex]k_{1}[/tex] is the propagation constant of transmitted wave.
The expression for the [tex]k_{1}[/tex] is given as:
[tex]k_{1}=\sqrt{\frac{2mE}{h^2} } \\\\=\sqrt{\frac{2(mc^2)E}{h^2c^2} } \\\\=\frac{\sqrt{2(mc^2)E}}{hc}[/tex]
Here [tex]m[/tex] is the electron mass; [tex]h[/tex] the reduced plancks constant; [tex]c[/tex] the speed of light and [tex]E[/tex] the energy of the incident wave.
substituting [tex]0.511\times10^{6}eV[/tex] for [tex]mc^2[/tex]; [tex]54.0eV[/tex] for [tex]E[/tex] and [tex]1.973\times10^{3}eV.A^{o}/c[/tex] for [tex]h[/tex] in the equation
[tex]k_{1}=\frac{\sqrt{2(mc^2)E}}{hc}\\\\=\frac{\sqrt{2(0.511\times10^{6}eV)(54.0eV)}}{1.973\times10^{3}eV.A^{o}/c}\\\\(3.765/A^o)(\frac{1A^o}{10^{-10}m})\\\\=3.765\times10^{10}/m[/tex] this is the propagation constant for the incident wave.
For [tex]K_{2}[/tex]
[tex]K_{2}=\sqrt{\frac{2m(U+E)}{h^2} } \\\\=\sqrt{\frac{2(mc^2)(U+E)}{h^2c^2} }\\\\=\frac{\sqrt{2(mc^2)(U+E)}}{hc}[/tex]
Here [tex]m[/tex] is the electron mass; [tex]h[/tex] the reduced plancks constant; [tex]c[/tex] the speed of light and [tex]E[/tex] the energy of the incident wave.
substituting [tex]0.511\times10^{6}eV[/tex] for [tex]mc^2[/tex]; [tex]64.0eV[/tex] for [tex]E[/tex] and [tex]1.973\times10^{3}eV.A^{o}/c[/tex] for [tex]h[/tex] in the equation
[tex]K_{2}=\frac{\sqrt{2(mc^2)(U+E)}}{hc}[/tex]
[tex]K_{2}=\frac{\sqrt{2(0.511\times10^{6}eV)(64.0eV)}}{1.973\times10^{3}eV.A^{o}/c}\\\\=(4.1/A^o)(\frac{1A^o}{10^{-10}m})\\\\=4.1\times10^{10}/m[/tex]this is the propagation constant for the transmitted wave.
substituting [tex]3.765\times10^{10}/m[/tex] for [tex]K_{1}[/tex] and [tex]4.1\times10^{10}/m[/tex] [tex]K_{2}[/tex]
[tex]R=(\frac{3.765\times10^{10}/m-4.1\times10^{10}/m}{3.765\times10^{10}+4.1\times10^{10}/m} )^2\\\\=0.0018[/tex]
The ratio of the reflected current to the incident current is the reflection coefficient.
[tex]R=(\frac{I_{reflected}}{I_{incident}}\\\\I_{reflected}=RI_{incident}[/tex]
substituting 0.0018 for R and 0.100mA for [tex]I_{incident}[/tex]
[tex]I_{reflected}=(0.008)(0.100)\\\\=0.18\times10^{-16}A[/tex]
