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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