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---------------------------- - 2307 - How Small is the Atom?
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- In the year 1811, Amedeo Avogadro, came up with an estimate of how small an atom was. Avogadro graduated from an Italian law school in 1796. He practiced law for three years and decided that physics was much more interesting.
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- In 1811 he published a theory that all gases at the same temperature and pressure have the same number of particles per unit volume. He understood the difference between atoms and molecules. In fact, it was Avogadro who coined the word “molecule”.
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- The molecular weight of hydrogen is 2, the atomic weight is one. That is because as a free gas two hydrogen atoms cling together to form a hydrogen molecule, H2. If we measure the volume of hydrogen gas at zero degrees Centigrade weighing the molecular weight of two grams it occupies 22.4 liters volume.
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- Oxygen has a molecular weight of 16, therefore 16 grams of Oxygen occupy the same volume of 22.4 liters and contain the exact same number of molecules. Since Oxygen also has two atoms per molecule, O2, the atomic weight of Oxygen is 8 and 8 grams would occupy exactly half the volume, or 11.2 liters. The number of oxygen atoms per unit volume would remain the same number. It is known as Avagodro’s Number.
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- It was not until 1865 the James Clerk Maxwell and Ludwig Boltzman made the first close calculations of Avogadro’s Number. Since we know the diameter of the atom to be 10^-10 meters we can make an estimate for ourselves of how many atoms are in 11.2 liters of gas. One liter is 10^-3 meters^3.
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- The volume occupied by the atom would be 10^-30 meters^3. Dividing we get 11.2 * 10^27 atoms in the gram-atomic weight of the gas. This calculation is not very precise, but you can see we get a very large number, 11 followed by 27 zeros.
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- Today, with precise measurements we know Avogadro’s number to be 6.02 * 10^23 atoms per gram-atomic weight of an element.
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- Every gram-atomic weight of every element and every gram-molecular weight of every substance as the same number of atoms, or molecules.
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------------------------ The number is 602,209,430,000,000,000,000,000 atoms.
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- This number applies to all elements, not just gases. For example, the atomic weight of carbon is 12. It weighs just 12 times as much as an atom of hydrogen. Twelve grams of carbon will have Avogadro’s number of atoms. Twelve grams is just under half an ounce, about the size of a spoon full of sugar. So if you visualize this spoon full of carbon, it will have exactly 6.02 * 10^23 atoms.
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- That is a very large number, and that many atoms in that small a space means atoms must be very small. If you had some very small tweezers and you could pick one atom out of the spoon every second. And, if you started at the time of the Big Bang, the birth of the Universe, you would not have enough time over those 13.7 billion years to pick out all the atoms in that spoon full of sugar.
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- In fact, the number of atoms removed would only be less than one millionth the number of atoms the carbon lump started with.
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------------------------- The number of seconds since the birth of the Universe is 4.32^10^17 seconds. 13.7 billion years times 3.16*10^7 seconds / year.
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------------------------- The number of atoms is 6.02*10^23. That leaves 6,019,995 *10^17 atoms left to count. 4.32 / 6,020,000 is less than 1 millionth, .717*10^-6.
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------------------------- Even continuing to pull atoms out at the rate of one every second you would need another 19,000,000 billion years to finish the job.
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-------------------------- 6.019995*10^23 atoms / 3.16*10^7 seconds = 19,050,619 billion years remaining to count the rest of the atoms.
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- Another way to visualize how many atoms are in that lump of carbon is to change them into pennies and give them out to every person in the world, 5 billion people would all be multi- trillionaires.
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------------------------ Each person would have 12 trillion dollars.
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------------------------ 6.02*10^23 pennies / 5*10^9 people = 1.205 *10^14 pennies per person which is 12.05 trillion dollars per person in the world.
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- Of course , you would have trouble distributing this many pennies. As you lay the pennies out on the table and shape them in the form of a disk, a giant disk. The disk of pennies would extend out to the orbit of the moon.
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- And, that would not be enough. You would have to stack them to get stacks 520 pennies thick for each stack to have enough total pennies.
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------------------------ A penny is 2 centimeters in diameter, 2*10^-2 meters.
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------------------------ The orbit of the Moon is 3.84*10^8 meters.
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------------------------ The area of a disk this size is pi*radius^2 = 46.3*10^16 meters^2.
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------------------------ The area that each penny occupies laying side by side = 4*10^-4 meters^2.
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------------------------ Dividing we get 11.58*10^20 pennies for the first disk.
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------------------------ In order to get 6.02*10^23 pennies we have to stack 520 disks on top of each other.
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- Another way to judge the size of an atom is to start with something familiar and start dividing it into equal parts. Let’s start with a meterstick, about the same as a yardstick. The smallest marks on the meter stick is a millimeter, 10^-3 meters, about the width of a pencil line.
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- If we divide the millimeter into a thousand equal parts we get a millionth of a meter, 10^-6 meters. This is called a micron. If you used a microscope, notice the same word “micro”, you could see bacterium, or cells, that would be about a micron in size.
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- If we divide a micron into a thousand equal parts we get a nanometer, 10^-9 meters. This is the size of lines, or etchings, in the integrated circuits that go into computers. Nanometer sized features are observed using electron microscopes because the wavelength of light is too long, at 400 to 700 nanometers. Far too big to resolve the features in an integrated circuit that are only 10 to 100 nanometers in length.
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- If we divide one nanometer into 10 equal parts we get down to the size of the atom that is 10^-10 meters in diameter. 10^-10 meters is called the angstrom. You can see why the computers are reaching physical limits using the current integrated circuit technologies. Just one tenth the size of a nanometer is the size of an atom.
- Instead of dividing we could multiply sizes and multiplying the size of an atom up to the size of an apple would multiply the size of an apple up to the size of the Earth.
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---------------------- The diameter of the Earth is 12.756*10^6 meters.
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---------------------- The diameter of a big apple is 10 centimeters, 10^-2 meters.
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---------------------- The diameter of an atom is 10^-10 meters.
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---------------------- To get from an atom to a big apple we multiply by 10^8.
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---------------------- Multiplying an apple diameter by 10^8 is 10^6 meters, about the size of the Earth, which is 12.7 * 10^6 meters in diameter.
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- All atoms are about the same size, 10^-10 meters. However, atoms themselves are mostly empty space. In fact, if you made the size the nucleus of an atom the size of a grape and set it in the middle of a football field, the electrons would be circling the grape at the end zones of either end of the field.
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----------------------- The size of the football field is 100 meters, 10^2 meters.
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----------------------- To go from the size of the atom, 10^-10 meters to the size of the football field we multiply by 10^12.
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---------------------- A nucleus is 10^-14 meters. Multiplying by 10^12 gets us to 10^-2 meters, or one centimeter, which is about the size of a grape.
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- If you lay on the floor and do five pushups you experience the force of gravity. The floor is pushing against your hands and your hands are pushing against the floor. Action equals re-action.
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- The atoms in the material of the floor is pushing against the atoms in the flesh and bones of your hands. But, this is not material against material. Actually, it is the electrostatic forces within the atoms that are doing the pushing because most of the atoms in the floor and in your hand are free space.
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- Of course, the vacuum of free space as not as simple as we think it is, but, that is another book review. Enough push ups? Ok, how about requesting another Review about a vacuum, ‘nothing” is not what you think :
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- March 13, 2019. 55
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--------------------- Thursday, March 14, 2019 -------------------------
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