Urban Teaching Resources: © Shawn Urban 29/02/12. CC BY-NC-SA 3.0

Page for Teachers and Discussion

 Twelve Lead Pencils The size of an atom and the number of atoms in Space are hard to visualize. This analogy makes these concepts more concrete.

Some Initial Concepts

How large is an atom? How many atoms are in the leads of 12 lead pencils?

Pencil leads are made of carbon atoms. Carbon has an atomic mass of 12.

Atomic mass is the mass of an atom. It is calculated as the sum of the number of protons and neutrons in the atom, because protons and neutrons make up the majority of the atom's mass. Each proton and neutron is given an atomic mass of 1. Since carbon has six protons and six neutrons, its atomic mass is 12. Carbon also has six electrons, but these are extremely light compared to the protons and neutrons and do not contribute to carbon's integral atomic mass.

Atomic mass is so light (1 atomic mass unit (amu) ∼ 1.66 x 10-24 g) that it is impractical to measure. Instead, scientists estimate atomic mass by measuring the mass of the element (in grams) which is equal in value to the number of protons and neutrons in an atom of the element. The amount of an element with this mass (in grams) is called a mole. An atom of carbon has an atomic mass of 12, so a mole of carbon weighs 12 grams. Placing 12 grams of carbon (pencil lead) beside 28 grams of silicon (sand) enables one to visually contrast the atomic mass of carbon (atomic mass 12) to that of silicon (atomic mass 28). (The comparison is not entirely visual, since element density influences the volume of a mole of an element.)

A mole of any element contains 602, 000, 000, 000, 000, 000, 000, 000 atoms of that element, that is 602 sexillion US, 602 trilliard UK or 6.02 x 1023 atoms. This number is called Avogadro's Number after Amedeo Avogadro (1776-1858) who discovered this number-of-atoms-in-a-mole relationship.

What does this have to do with 12 pencil leads?

Twelve pencil leads weigh approximately 12 grams, so have 6.02 x 1023 atoms in them.

But what does 6.02 x 1023 atoms mean?

Green Pea Analogy

It's a lot, yes. But how much is a lot?

The number of carbon atoms in 12 pencil leads can be visualized if in our minds we enlarge one carbon atom to the size of one green pea, those things we find in pods and eat as vegetables (peas are actually fruit, but that is another story).

With this comparison in mind ... (Note: The cells in this table are to be revealed sequentially rather than en mass. Students love throwing out guesses as this table iterates to Avogadro's Number.)

ExponentValueAnalogy
100  1  One pea
101  10  10 peas - spoonful
102  100  10 spoonfuls of peas - plateful
103  1000  10 platefuls of peas - bag
104  10 000  10 bags of peas
105  100 000  100 bags of peas - fridgeful
106  1 000 000  10 fridgefuls of peas - an average bedroom
107  10 000 000  Average house full from basement to attic with peas
109  1 000 000 000  100 houses full from basement to attic with peas - a small village
1012  1 000 000 000 000  100 000 houses full from basement to attic with peas - a small city
1015  1 000 000 000 000 000  A large city like New York covered 1 m deep with peas
1018  1 000 000 000 000 000 000  A province like Alberta covered 1 m deep with peas
1020  100 000 000 000 000 000 000  The land mass of Canada covered 1 m deep with peas
1021  1 000 000 000 000 000 000 000  The land mass of the world covered 1 m deep with peas
1023  100 000 000 000 000 000 000 000  The entire surface of the earth plus 99 planets just like earth covered 1 m deep with peas
6.02 x 1023  602 000 000 000 000 000 000 000  602 planets like earth covered 1 m deep with peas = 12 pencil leads = one mole of carbon atoms = 1/18 the surface area of the Sun

You may be interested in a Slideshare Presentation created by Pak Liam in response to this table. The Slideshare is part of Pak's science resources page of his blog.

Summary Concepts

Four things become very obvious from this analogy:

1. Hover Point: Atoms are very, very small!

2. Hover Point: There are a lot of them!

3. Hover Point: Our Sun is very, very big!

4. Hover Point: The Universe is incredibly large, and to think, if the Big Bang theory were believed, the Universe began much, much smaller than an atom!