The four graphs below represent wave functions of an electron in an Infinite one

Question

The four graphs below represent wave functions of an electron in an Infinite one-dimensional square well of width L = 0.13 nm. The wave functions are of course, zero outside the well. For 0 lessthanorequalto x lessthanorequalto L the wave functions all have the form N sin(2 pi x/lambda), where N is the normalization constant, and lambda is different for each wave function. For each of the four wave functions find the wavelength. lambda and the energy, E, of the electron. Assume that the potential energy within the well is zero. Wave function 1: lambda Wave function 2: Wave function 3: Calculate N. (It's the same for all four wave functions.)

Explanation / Answer

case 1) lambda = 4L=4*0.13=.52mm

energy= E= planks constant2*k2/(2*m)

where, k=n*pi/L

case 1 has n=1

plank's constant=6.626*10-34 m2 kg/s

mass of electron= 9.109 *10-31 kg

E=1.47*10-34 J

case 2,n=3

wavelength=L=.13mm

E=4.41*10-34J

case 3,n=4
lambda=L+.25L=.1625mm

E=5.55*10-34 J

case 4,n=6

lambda=2*L=.13*2=.26mm

E=8.82*10-34 J

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