Download little number number lines 17-18

17th Problem
LITTLE NUMBERS
We now wish to investigate “size” on an atomic scale.
For perspective: a typical human hair is about 1 million
carbon atoms in width. A single drop of water contains
about 2x1021 (2 sextillion) atoms of oxygen and 4
sextillion atoms of hydrogen. If an apple were
magnified to the size of the earth, then the atoms in it
would be about the size of the original apple.
Consider the table below containing weight information
of 8 common elements:
SYMBOL = ELEMENT
(Atomic Number)
H = Hydrogen (1)
Na = Sodium (11)
O = Oxygen (8)
Cl = Chlorine (17)
Fe = Iron (26)
Au = Gold (79)
Rn = Radon (86)
U = Uranium (92)
Spring 2010 NPO
WEIGHT
(in grams)
1.674 x10-24
3.818 x10-23
2.657 x10-23
5.887 x10-23
9.208 x10-23
3.271 x10-22
3.687x10-22
3.953x10-22
WEIGHT
(in g/mole)
1. Because the weight of an atom is so small, the
weight of a mole of an element is often used,
where a mole consists of 6.022x1023 (Avagadro’s
number) atoms. Convert the weights in the table
above into grams per mole.
2. Plot the weights of the elements from the table
using units of grams per mole on the number line,
labeling the points with the atomic symbols
Your graph should look something like the number
line below:
0 HONaCl
Fe
Spring 2010 NPO
Au
RnU
300
18th Problem
LITTLE NUMBERS
We now look at the size of atoms by plotting the atomic
radii of some elements on the number line. The table
below contains the radius of each of the 8 elements
considered in the preceding problem. The
measurements are given in picometers, i.e. trillionths of
a meter.
ELEMENT
ATOMIC RADIUS
ATOMIC RADIUS
(Atomic number) in pm (trillionths
in units
=10-12 of a meter)
H = Hydrogen(1)
53
1
Na = Sodium (11)
190
O = Oxygen (8)
48
Cl = Chlorine (17)
79
Fe = Iron (26)
156
Au Gold (79)
174
Rn = Radon (86)
120
U = Uranium (92)
175
Spring 2010 NPO
1. If we define one unit to be the radius of the
Hydrogen atom, complete the third column of the
table.
2. Plot on a number line the radii of the atoms (in
units) from the table above, labeling them with
their atomic symbols.
Your graph should like similar to the following:
0
OH
Cl
Rn
Fe AuU Na
Atoms themselves are made up of smaller elementary
particles called neutrons, protons, and electrons.
3. If we choose the radius of a proton, which is 1.1133
fermis (10-15m), to be our unit, what would the
radius of Hydrogen be in units in such a system?
4a. If we choose the radius of an electron, which is
9.087x10-17m, to be our unit, what would the radius
of a proton (in units) be in this system?
Spring 2010 NPO
5
4b. What would be the radius of a neutron, which is
1.1128 fermis, in this system?
4c. What would be the radius in this system of the
Hydrogen atom (which is composed of one proton
orbited by one electron)?
OPEN RESPONSE: describe what relationship(s), if any,
you see between the atomic number, size and
weight of the atoms in this problem.
Spring 2010 NPO