Suppose an electron is confined to a one-dimensional box of length 10 nm, and that it is in the first excited state (n = 2; remember n = 1 is the ground state!). a) what is the probability that the electron will be found between x = 0.1 and 0.2 nm? (hint: identify the correct wavefunction to determine the probability density function. Since there is only 1 dimension, this is the probability per unit length, which you should integrate between the limits of interest. The integral you need is found in Justification 9.1 in the text, or you can use an online calculator) b) what is the probability that the electron will be found between x = 4.9 and 5.2 nm? c) what is the energy of the electron? d) what wavelength of light would be required to excite this electron into the 2nd excited state (n = 3)?
