Introduction & Purpose:
What is an isotope? What does it mean to say that the atoms in a sample of an element are isotopes of each other? Ordinary beans are a lot bigger than atoms, but perhaps they can give you one or two clues about isotopes.
We have talked in class about isotopes: atoms of the same element that differ in mass. For example, there are actually three different kinds of hydrogen atoms. Refer to the table below for the different kinds (or isotopes) of two common atoms.
ISOTOPE
Protium
Deuterium
Tritium
Carbon-12
Carbon-14
PROTONS ELECTRONS NEUTRONS SIGNIFICANCE
1 1 0 “normal” hydrogen
1
1
1
1
1
2
“heavy hydrogen”
radioactive hydrogen
6
6
6
6
6
8
“normal” carbon
carbon-14 dating
This lab exercise is designed to show you isotopes of an element in a simulation form.
You will be asked to gather data about the “isotopes” and organize the data. If atoms were as large as beans they could be sorted, counted, and massed. In this experiment we will sort, count, and mass three different kinds of beans and imagine that we are observing three different isotopes of the same element (let’s call it
BEANIUM). The three different isotopes are blackium, brownium, greenium and whitium. Finally we will calculate the isotopic mass, the isotopic abundance, and the atomic mass of the bean element.
These experiments and calculations are equivalent to the way scientists actually determine the atomic mass of elements. As in real elements, the mixture of isotopes are collections of atoms of the element each having different masses because they have different numbers of neutrons. Unlike real isotopes, the individual isotopic particles of Beanium differ slightly in mass, so you will determine the average mass of each type of isotopic particle. Then you can calculate the
"weighted average atomic mass" of Beanium.
Beanium Lab 1

Definitions/ reference:
 Isotopic mass – the average mass of the atoms of a specific isotope of an element
 Isotopic abundance – what percent of the element’s atoms are a specific isotope
 Atomic mass – the average mass of an element’s atoms
#Protons: determine which element an atom is – determines the atomic number
# electrons: determine the charge on an atom
Protons = electrons – atom is neutral
Protons> electrons – atom is positively charged (lost electrons)
Protons< electrons - atom is negatively charged (gained electrons)
# neutrons – determines the atomic mass of an atom. Determines the isotope number of the atom.
Isotope: an atom of an element with a certain number of neutrons.
NOTE: All atoms of an element are isotopes of that element.
Most elements have 1, 2 or 3 naturally occurring isotopes. This means that in any sample of the element these naturally occurring isotopes are all present typically always in the same % ratio.
For example:
The element carbon has three isotopes:
12
6
C = 6 neutrons and is called Carbon -12 isotope 90% abundance
13
6
C = 7 neutrons and is called carbon-13 isotope 9% abundance
14
6
C = 8 neutrons and is called carbon-14 isotope 1% abundance
% abundance means that in a sample of carbon (like a lump of coal or a diamond) 90% of the carbon atoms will be carbon-12, 9% will be carbon-13 and 1% will be carbon-14.
Since not all the atoms in a sample of an element have the same mass, we have to calculate an average atomic mass for the element. The average atomic mass is calculated taking into account the different percents of each isotope present.
Beanium Lab 2

Materials: Plastic cup or ziplock bags of beans (black, brown, & white); electronic balance
Procedure:
1.
Obtain a plastic cup which contains many atoms (beans) of BEANIUM.
2.
Sort the atoms (beans) into a group for each isotope: black, brown, white.
Record the total number of atoms and the number of each type of isotope
(blackium, brownium, greenium and whitium) in the data table.
3.
Determine the isotopic mass: a) find the total mass of each of the three isotope groups and record on data table b) find the average mass of a single atom of each isotope and record on the data table to the nearest 0.001g.
EXAMPLE : I counted 340 white beans. They have a mass of 80 grams. The average mass of one white bean is 80 / 340 = 0.235 grams.
4.
Find the isotopic abundance (% of beans) for each isotope by dividing the number of atoms of one isotope by the total number of atoms (black, brown, plus white) and multiplying by 100%. Record on the data table to the nearest
0.1%.
EXAMPLE : There are a total of 500 atoms. 340 are white beans. Therefore, (340 ÷
500) x 100% = 68.0% are white beans (whitium).
5.
Determine the atomic mass for BEANIUM based on the isotopic abundances and the isotopic masses.
FORMULA TO CALCULATE ATOMIC MASS = (blackium %) x (mass of one blackium atom) + (brownium %) x (mass of one brownium atom) + (whitium %) x
(mass of one whitium atom)
6.
Place all the beans back in the plastic cup or ziplock bag.
Data:
 Show one sample of each calculation. Remember significant digits for all calculations.
 Complete the data table.
Beanium Lab 3

Name: __________________________ Date: _____________ Period: _____
DATA TABLE
Isotope information: Total number of bean element atoms in cup = ________
ISOTOPE # OF BEANS
(ATOMS)
MASS OF BEANS
(ATOMS)
AVERAGE MASS OF
ONE BEAN (GRAMS)
% OF
BEANS
Blackium
Brownium
Greenium
Whitium
Calculations for atomic mass of BEANIUM…(use the data table to complete)
Analysis Questions:
1.
What is an isotope?
2.
Explain any differences between the atomic mass of your BEANIUM sample and that of a different lab group. Explain why the difference would be smaller if larger samples were used.
3.
What is the relationship between an element’s isotopes and the element’s atomic mass?
4.
What is meant by a weighted average?
5.
How are the beans in this lab similar to isotopes? How are they different?
6.
What are at least two sources of error for this activity. (A source of error is
an error that could have affected your results.)
Beanium Lab 4

Isotopes and Weighted Average Atomic Mass
If the atomic mass is the sum of protons and neutrons in an atom, why are the atomic masses on the periodic table not all whole numbers? Because the atoms of elements come in a variety of isotopes, meaning they are made up of atoms with the same number of protons
(atomic number) but different number of neutrons in the nucleus. The atomic number on the periodic table is a “weighted average” of the naturally occurring isotopes of that element.
The weighted average atomic mass (sum of neutrons and protons) takes into account the fact that there are different amounts of each type of isotope (abundance) in a naturally occurring sample of any given element. The weighted average atomic mass is calculated by multiplying the decimal equivalent of each isotope times its mass and adding up all the results for all the naturally occurring isotopes.
AMU = atomic mass unit = mass of one proton = mass of one neutron
Example:
A sample of Cesium, Cs, has the following % abundance:
Cs-132 = 20.0%; Cs – 133 = 75.3%; Cs – 134 = 4.7%
Weighted average atomic mass = (0.753 x 133) + (0.20 x 132) + (134 x 0.047) = 132.85 amu
Determine the average atomic mass for the following mixtures of isotopes:
1.) Au – 197 = 50%, Au 198 = 50%
2.) Fe – 55 = 15%, Fe – 56 = 85%
3.) H – 1 = 99%, H-2- = 0.8%, H – 3 = 0.2%
4.) N-14 = 95%, N-15 = 3%, N-16 = 2%
5.) C-12 = 98%, C-14 = 2%
Beanium Lab 5