Tucked into Lecture 5 is an important result we now come back to. To recap: in order to calculate the average value of something (e.g. 'x') when we know the individual probabilities of the system possessing each of every possible value (px_i) we have: = px_i X. Wavefunctions give us probabilities of having a certain position, but they are continuous rather than discrete probabilities, therefore the average position is given not by a sum but (r) = Sallspace rub(r, 0, 6) av by an integral: calculate: where dV is a volume element. Use this to a. the average distance of the electron from the nucleus in the 1s orbital of hydrogen b. the average distance of the electron from the nucleus in the 2s orbital of hydrogen c. The ratio of the 1s distance over the 2s distance (only this will be input on BBLearn).