1. How many isotopes?
There are 81 elements with at least one stable isotope; 279 stable isotopes in all.
All elements above atomic number 83 (Bi) are unstable; their isotopes are radioactive.
Most elements have 2-4 stable isotopes.
In a population of atoms of a single element, some isotopes are common, others are rare.

2. Atomic Mass

3. 99.98% 0.02% trace Natural Abundances
For example,
99.98% 0.02% trace Natural Abundances

4. Atomic Mass
A sample of an element usually contain several isotopes of that element that have different masses.
The % abundances for elements are well known and do not change significantly over time.
The atomic mass of an element is the weighted average of the naturally occurring isotopes of that element.

5. Atomic mass is not the same as mass number!
On your periodic table, the atomic mass is near the top left corner of each element’s box
Atomic mass is not the same as mass number!

6. Another Wrinkle
Not all protons and neutrons have exactly the same masses!
The lighter elements have nucleons (protons and neutrons) that tend to have slightly higher masses than the heavier ones.
Most elements (except H, He, and Li) are created in stars during the nuclear fusion process.
A small bit of mass is converted into energy according to Einstein’s famous equation E=mc2

7. The Solution to the Mass Problem
Because of this, relative masses are used. The masses of protons and neutrons are compared to an atom of Carbon-12.
Each carbon-12 atom is given a mass of atomic mass units (amu).
A single proton or neutron of carbon-12 has a mass of amu. All other protons and neutrons are slightly higher or lower.

8. Average Atomic Mass
The atomic masses of individual isotopes, along with their % abundances, are used to calculate the average atomic mass of an element.
The average atomic mass is a weighted average, like many teachers use to calculate your grades.

9. Problem
What is the average atomic mass of chlorine, given that it’s naturally occurring isotopes have the following masses and abundances:
Isotope
(nuclide)
Atomic mass
(amu)
% Abundance
35Cl
75.77%
37Cl
24.23%
Note that the mass numbers of the nuclides are slightly more than their masses in amu.
This is known as the “mass deficit,” where a bit of matter was converted into energy when nuclear fusion in aging stars created the chlorine atoms.

10. Problem 1
Chlorine has two naturally occurring isotopes. 35Cl is 75.77% of chlorine atoms, and has a mass of amu. 37Cl is 24.23% of chlorine atoms, and has a mass of amu.
Showing a correct numerical set-up, determine the average atomic mass of chlorine.

12. Calculating Average Atomic Mass
Isotope
(nuclide)
Atomic mass
(amu)
% Abundance
35Cl
75.77%
37Cl
24.23%
Make a table (if necessary)
Multiply the atomic mass of each element by its abundance.
Sum the two products.
Divide the sum by 100.
Check your periodic table to see if you are correct.
Ms. Costello’s acronym: M – A – D: multiply, add, divide!

13. Doin’ the Math Isotope (nuclide) Atomic mass (amu) % Abundance 35Cl
75.77%
37Cl
24.23%
Products
/100 = amu

14. Problem 2
Lithium has two naturally occurring isotopes. Lithium-6 composes 7.42% of lithium atoms, and has a mass of amu. lithium-7 is the rest (92.58%), and has a mass of amu.
Showing a correct numerical set-up, calculate the average atomic mass of lithium.

15. Problem 3
Oxygen has three naturally occurring isotopes. Using the table below, show a correct numerical set-up for calculating the average atomic mass of oxygen.
Isotope
Atomic mass (amu)
% abundance
16O
15.994
99.76%
17O
16.999
0.037%
18O
17.999
0.204%

16. Lab 3: Average Atomic Mass of “Pennium”
Materials: Digital balance, 33 pennies
Procedure:
Take a balance and 33 pennies from the can at random.
Measure the mass of each penny and make a data table of your measurements.

17. Calculations
Group the pennies with similar masses (±0.1 g) together as an “isotope.”
How many isotopes do you have?
How many pennies of each isotope do you have?
Calculate the average mass of each isotope. Show work below for each isotope.
Calculate the percent abundance for each isotope. Show work below.
Using the average mass of each isotope, calculate the average atomic mass of pennium. Show work below.

18. Pennium Lab Questions
Why are the masses of pennies different from each other? Use data in Table S to explain your answer.
A student made the following statement: “According to the periodic table, the mass number of calcium-40 is ” This is incorrect. Explain why it is incorrect.
Copper has two naturally occurring isotopes, Cu-63 (62.93 amu, 69.09% abundance), and Cu-65 (64.93 amu, 30.91% abundance). Show a correct numerical set up for calculating copper’s average atomic mass.

19. Using the density of copper (table S), calculate the volume of an old penny, in cm3, showing work below.

20. Using your volume measurement from question four, calculate the density of zinc using one of the lighter pennies. Show your work.

21. Using your calculation for the density of zinc from question 5, calculate your % error using the accepted value of zinc’s density from Table S. Show work.

22. Castle Learning Homework Assigned Monday 9/30 Due Wednesday 10/2
Atomic Theory (33 Multiple Choice Questions)
Type in user name (npz-first initial last name)
Don’t type in password – it will prompt you!
Have your reference tables, periodic tables handy
Atomic Theory Test on Friday, 10/4
30 multiple choice questions, nuclide table, atomic mass problem, a few short answers

23. Homework Problem 1
Using the following table, show a correct numerical setup for calculating the average atomic mass of chromium.
Isotope
Atomic mass (amu)
% abundance
Chromium-50
49.95
4.31%
Chromium-52
51.94
83.76%
Chromium-53
52.94
9.55%
Chromium-54
53.94
2.38%

24. Homework Problem 2
The table below gives information about two isotopes of element X.
Calculate the average atomic mass of X. Identify the element.
Isotope
Mass
(AMU)
Relative Abundance
X-10
10.01
19.91%
X-11
11.01
80.09%