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If you look up "size" in the dictionary, it will say something
like: "The physical magnitude, extent, or bulk of something."
The basic dimensions of measurement are length, mass and time.
The derived dimensions are area, force, etc. For our purposes,
we will focus primarily on length, though we will also discuss
the others briefly.
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| Figure 1: The diversity
of the size of objects in our Universe. Roll your mouse
over the images for more information about their sizes.
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It is fairly simple to imagine the length of a meter, just
look at the length of your arm. You can walk 1000 meters in about
15 minutes, or drive the same distance in about a minute. However,
when lengths get longer than what we can personally experience,
such as the distance from the Earth to the sun, or the diameter
of the universe, it becomes difficult to comprehend.
Our eyes generally give us the ability to discern things as
small in size as an ant's eye and the point of a pin (approximate
size 50 µm). About 300 years ago, with the invention of
the light microscope it was discovered that there is a whole
new world of living organisms much smaller than a pinpoint.
Recently developed microscopes, such as the scanning probe microscope
(SPM), allow us to visualize and study even smaller objects,
including individual atoms.
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One way to think of scale is the relationship between the actual
length you are measuring, and the way that length is represented
numerically or visually. A scale has a succession of ascending
and descending steps, or relative dimensions, used to assess
the absolute or relative size of some property of an object,
such as length, temperature, or mass. The unit of measurement
for measuring length can be inches, feet, rods, meters or one
of many other traditional units of length. The unit of measurement
for temperature can be degrees Fahrenheit, degrees Celsius or
Kelvin. Weight can be measured in pounds, grams, tons or other
units of mass.
Scales can range from smaller than an atom to larger than
the universe and hence, a linear scale is not a convenient
representation. A logarithmic scale, however, uses the Power
of 10 to represent and compare the relative size or distances
of objects with actual lengths that are so drastically different
that it would be difficult to represent them on a linear scale.
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| Figure 5: In a
linear scale, the lengths represented between each of
the two equi-distant marks is equal. So, the distance
between 1 and 2 is the same as the distance between 3
and 4. The map scale is linear scale. |
Remember that each step, in a logarithmic scale, differs by
one order of magnitude from its preceding or the succeding step.
Look at the illustration of a logarithmic scale below.
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| Figure 6: In this
scale the length represented between 1 and 2 is 10 times
longer than the length between 0 and 1. Similarly, the
length represented between 2 and 3 is 10 times longer
than the length represented between 1 and 2 and 100 times
longerthan the length represented between between 0 and
1. Each step in the logarithmic scale is an order of magnitude.
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| Figure 7: A pH
scale, which you have already studied about in your chemistry
class, is based on the logarthmic scale. In the scale
above, the pH of distilled water is 7. On going to the
left, in the direction of increasing acidity, we encounter
lemon juice with a pH = 3.7, and sulphuric acid with a
pH = 0.5. If the above scale were a linear scale, like
the everyday ruler, we would be led to believe that sulphuric
acid is only about seven times stronger than lemon juice.
Since, the scale is logarithmic in nature, sulphuric acid
is in reality, more than a 1000 times powerful than lemon
juice. It is so powerful that it can chew away metals
too. |
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How small is small? It depends on how small you are. A
bee is small. You can squish one with the tip of your
finger, if you are careful! But compared to a pollen grain
collected by the bee, then the bug is big! In fact a bee
is considered to be at the macro-scale, the pollen grain,
which can be seen only with the aid of a microscope, is
at the micro-level. This is getting down there. So how
low do we need to go until we are talking small? How about
the size of the pore on the pollen grain? Are we talking
small yet? Yeah, but we are still not at the nano-scale!
The nano-scale begins at 10 nanometers in length and a
nanometer is one-billionth of a meter.
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| Figure 9:
(a) A bee is small to us, only about 12 mm in length.
(b) The pollen grains are so small that thousands
of them can be stuck to just one leg of the bee.
(c) Individual pollen grains are not visible without
microscopes. Each of these is about 30 µm in diameter,
but they are still not small enough to be considered
nano-scale. (d) The individual pores on the surface
of this pollen grain are only about 1 µm in diameter,
but that is still 100 times too big to be considered
nanoscale. |
How many pollen grains can fit on the head of a pin?
How about on the point of the pin? In this activity,
compare the size of different biological samples to
the size of the point of a pin. Use the measure tool
to compare how many of each sample it takes to cross
the top of the pin point.
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How big is big? It depends on how big you are, or the scale
for which you are using for your comparison.
If you are the size of the Earth, then the moon may seem
small. But the sun is pretty big. But compared to the size
of the universe, the sun is miniscule. In this activity compare
the size of different planets in our solar system to the sun.
Use the measure tool to compare how many of each of the planets,
or Shaq, a mere human here, would equal the distance across
the diameter of the sun.
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Things at different scales can look very similar. So you
may not be able to tell what it is, if you don't know
the scale. Also, some things look very different at different
scales, which can also be confusing. It is helpful to
know what the scale is for something you are studying.
Figure 10:
These images look similar, but they
have drastically different scales. One image has
a scale of 1 500 m across and is an ice-free trough
in the north polar ice cap of Mars taken from
the Malin Space Science Systems/NASA. The other
image is of the surface of videotape as "seen"
with a Magnetic Force Microscope (MFM). It is
only 65 µm across. Can you tell which is the larger
object from the images?
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| Figure 11:
(a) A penny. (b) The word "TRUST" on the penny.
(c) The letter "R" in the word "TRUST". If you saw
only the microscopic image of the letter "R", would
you know what you were looking at? However, if you
were given the scale, 0.7 mm, you would at least
know you were looking at something about the size
of the letter "R". |
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Whichever type of scale you use the units of measurement represented
on it are all defined. A meter, an inch, or a gallon did not
come from nature but were devised by people who needed to measure
things. As people needed to measure things more precisely, universally
accepted measurement units were needed.
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Figure 13:
The 18th century French Academy of Sciences was
responsible for developing and defining the original
meter.
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Figure 12:
Not every person's foot is the same length, so folks
had to decide just how long an inch, foot, mile
and other lengths really were.
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In the late 1700s, the French National Assembly directed the
French Academy of Sciences to replace the confusing welter of
traditional but illogical units of measure with a rational system
based on multiples of ten. They chose to call this new basic
unit of measurement a "meter," based on the Greek word, "metron,"
which means "to measure." The new meter was defined as one ten-millionth
of the distance along the meridian running from the North Pole
to the equator through Dunkirk, France and Barcelona, Spain.
Their laborious six-year survey to determine the distance yielded
a meter equal to 39.37008 inches. However, it was later discovered
that the length of the meter they defined was off by 0.2 millimeters.
That may not seem like much until you consider that means their
survey was off by 2000 meters!
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Figure 14: The
first estimates of a meter were obtained, by an extensive
survey, around the globe.
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As technology improved, the meter was defined as 1,650,763.73
times the wavelength of the orange light emitted when pure
krypton gas, of the isotope with mass number 86, is excited
with an electrical discharge. Currently, a meter is described
as the distance that light in a vacuum will travel in 1/299,792458th
of a second.
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Arizona State University
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