What is size?

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.

Figure 1: The diversity of the size of objects in our Universe. Roll your mouse over the images for more information about their sizes.

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.

What is scale?

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.

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.

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.

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.

Little by little

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.

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.

On a grand scale

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.

"What the scale?"

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?

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".

Meters matter

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.

Figure 13: The 18th century French Academy of Sciences was responsible for developing and defining the original meter.

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.

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!

Figure 14: The first estimates of a meter were obtained, by an extensive survey, around the globe.

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.

[ Home | ModuleMap | Tips | Glossary ]