Problem
An electron is trapped in an infinite well that is 100 pm wide and is in its ground state. What is the probability that you can detect the electron in an interval of width ?x=5.0 pm centered at x= (a) 25 pm (b)50 pm (c)90 pm ?
P(x) =|?(x)|2 is probability/unit length
P(x)dx = probability that electron is located in interval dx at x
L=100 x 10-12 m ?(x)=(2/L)1/2 sin(?x/L)
P(x) ?x = (2/L)sin2(?x/L) ?x =(1/10) sin2(?x/L)
a) P(x) ?x =.1 sin2(?/4) = .05
b) P(x) ?x =.1 sin2(?/2) = .1
c) P(x) ?x =.1 sin2(.9?) = .0095