An electron confined to a one-dimensional box has energy levels given by the equation En = n2h2>8 mL2

where n is a quantum number with possible values of 1, 2, 3,â€¦, m is the mass of the particle, and L is the length of the box.

a. Calculate the energies of the n = 1, n = 2, and n = 3 levels for an electron in a box with a length of 155 pm.

b. Calculate the wavelength of light required to make a transition from n = 1Â¡n = 2 and from n = 2Â¡ n = 3.

In what region of the electromagnetic spectrum do these wavelengths lie?