# Homework 16 (Due 5/18/2016)

- Page ID
- 47397

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:

- Probability of finding an electron in hydrogen in the 1s orbital at a radius between \(a_o\) and \(2a_o\)
- Probability of finding an electron in hydrogen in the 2s orbital within a radius of \(\frac{a_o}{2}\)
- The most probable radius for an electron in hydrogen in the 2s orbital.
- The probability of finding an electron in the \(n=1\) and \(l=0\) of being outside the Bohr Radius.
- 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 *m _{s}* 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:

- N
- Si
- Fe
- Te
- 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.