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a. A particle of mass m moves freely in a one-dimensional box of length 3a. In the same diagram, sketch the wave function and the squared wave function for the 2nd excited state of the particle and show the positions at which the nodes occur. (5 marks) N b. An electron (m= 9.1 x 10-31 kg) is confined to a one-dimensional box of length 4.0 x 10-ºm. Calculate the energy gap between the ground state and the 1st excited state of the electron. What wavelength corresponds to a spectral transition between the two states? (5 marks)
c. Write the mathematical expression for the radial probability function. The radial probability function for any orbital is zero at the nucleus, it also approaches zero at long distance from the nucleus. Explain why. (5 marks)