Question

The wave functions for thee 1s and 2s orbitals are as follows 1s 2s 3/2 where ao is a constant (ao -53 pm) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the difference sin the pots and identify thee node in the 2s wave function (10 pts)

Answer 1

From given data psi = (1/pi)^1/2 (1/a_0^3/2) exp (-r/a_0) psi = (1/32 pi)^1/2 (1/a_0^3/2) (-2r/a_0) exp (-r/a_0) We need to identify the wave function of 2s: a_0 = 53 pm rightarrow constant psi 2s = (1/32 pi)^1/2 (1/a_0^3/2) (2 - r/a_0) exp(r/a_0) The only variable in the above equation is r at the node psi 2s = 0 This will be possible at the node if (2 - r/a_0) = 0 (or) r/a_0 = 2 (or) r = 2a_0