Help! Consider an electron that can exist only between x = 0 and x = L = 8.5nm o

Question

Help!

Consider an electron that can exist only between x = 0 and x = L = 8.5nm on the x axis. We could say that this electron is confined to a "box" of length L. In this situation, imagine the standing de Broglie waves that can fit into the box. For example, the drawing shows the first three possibilities. Note in this picture that there are either one, two, or three half-wavelengths that fit into the distance L. For each of these cases find kinetic energy of the particle. Number *1 Units Number *2 Units Number *3 Units

Explanation / Answer

p = h/lambda

p = sqrt(2*m*K.E)

K.E = p^2/2m = h^2/(2m*lambda^2)

h^2/2m = 2.22*E-37

a)lambda = 2L = 17 nm

K.E = 7.69*E-22 J = 4.8*E-3 eV

b) lambda = L = 8.5 nm

K.E = 30.76*E-22 J = 19.225*E-3 eV

c)lambda = 2L/3

K.E = 69.21*E-22 J = 43.25*E-3 eV

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