Homework 8

Textbook Problems: 42-27, 42-28, 42-34, 43-5, 43-22.

Question

Give a short (1/2 to 1 pages) answer to the following question:

1) How would the atomic shell structure be affected if electrons did not obey the Pauli Exclusion Principle?

Physics/Math:

Consider the n=2, l=1, $m_l= 0, \pm 1$ wave functions for hydrogen:

$$\psi_{210} = C_{210} \frac{r}{a_o} e^{-r/2a_o} \cos \theta$$ (1)

$$\psi_{21 \pm 1} = C_{211} \frac{r}{a_o} e^{-r/2a_o} \sin \theta e^{\pm i \phi}$$ (2)

a) Find the probability per unit length ($\mid \psi \mid ^2 r^2$) and determine the maximum.

b) Single out and describe the spatial (rotational) symmetries of $\mid \psi \mid ^2 r^2$ in both cases.