# Homework 16 (Due 5/18/2016)

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

## Q16.1

Which quantum numbers influence the energy of a specific electron in a hydrogen atom? What about for a lithium atom? If there is a different, why?

## Q16.2

Write the integrals/equations that need to be solved (do not solve) to calculate the following values:

1. Probability of finding an electron in hydrogen in the 1s orbital at a radius between $$a_o$$ and $$2a_o$$
2. Probability of finding an electron in hydrogen in the 2s orbital within a radius of $$\frac{a_o}{2}$$
3. The most probable radius for an electron in hydrogen in the 2s orbital.
4. The probability of finding an electron in the $$n=1$$ and $$l=0$$ of being outside the Bohr Radius.
5. The probability of finding an electron in the $$n=2$$ and $$l=1$$ of being outside the Bohr Radius.

## Q16.3

How many electrons could be held in the second shell of an atom if the spin quantum number ms could have three values instead of just two? (Hint: Consider the Pauli exclusion principle.)

## Q16.4

Write a set of quantum numbers for each of the electrons with an n of 4 in a Se atom.

## Q16.5

Use an orbital diagram to describe the electron configuration of the valence shell of each of the following atoms:

1. N
2. Si
3. Fe
4. Te
5. Mo

## Q16.6

What are number of radial, angular and total nodes for all wavefunctions in the first three shells ($$n \le 3$$) of hydrogen atom. What are the general equations relating the number of radial angular and total nodes as a function of quantum numbers.

## Q16.7

Explain the general trend and rational between $$Z$$ and $$E_{eff}$$ for the outermost (valence) electron and core electron (i.e., $$n=1$$) in the first 20 elements of the periodic table.