FIGURE P39.31 shows the wave function of a particle confined between x = 0 nm and x = 1.0 nm. The wave function is zero outside this region.

a. Determine the value of the constant c, as defined in the figure.
b. Draw a graph of the probability density P(x) = |ψ(x)|².
c. Draw a dot picture showing where the first 40 or 50 particles might be found.
d. Calculate the probability of finding the particle in the interval 0 nm ‰¤ x ‰¤ 0.25 nm.