16: Cobalt has atomic number 27. This means that all isotopes of cobalt have 27 protons. Thus Cobalt 59 has 27 protons and 59 - 27 = 32 neutrons. Cobalt 60 has 27 protons and 33 neutrons. Both isotopes, if neutral, have 27 electrons.
22: Gold has atomic number Z=79. If you add one proton, you get Z=80 or mercury. If you subtract a proton, you get Z=78 or platinum. Thus subtracting one proton from each nucleus would be more valuable than adding one.
Chapter 13:
Project: Eggs sink in water. You need to dissolve a LOT
of salt in water to make an egg float. This means that an egg is
denser than fresh water but less dense than salt water (if there is enough
salt in the water). This is a fun project to do with children.
Exercises:
10: The blocks of metal both sink. This means that they displace
their volume of water. Both blocks have the same volume so they displace
the same amount of water. The lead is heavier, but that does not
matter since it is not floating.
12: The blocks of metal still both sink. Lead is denser than aluminum so that a 10 N block of lead (about 1 kg or 2 pounds) takes up less volume than a 10 N block of aluminum. (This is more obvious if you think about styrofoam and metal. You need a much bigger piece of styrofoam to weight the same as a piece of metal.) Since the lead takes up less volume, it displaces less water than the aluminum. The difference is that in this problem the blocks have the same weight, not the same volume.
18: The stones hurt your feet less in deep water than in shallow water because more of your body is underwater (ie: you are displacing a larger volume of water) so that there is a larger buoyancy force. There are three vertical forces acting on your body: gravity, buoyancy, and the normal force from the stones. Since the net vertical force on you is zero, the normal force from the stones equals gravity minus the buoyancy force. The more buoyancy, the less normal force and the less pain.
Problems:
2: Density = mass/volume = 6 kg/ 1 l = 6 kg / 0.001 m^3 = 6000 kg/m^3.
6 kg/l is also an acceptable answer (but you would lose 1 point on
a test because I want the answers in standard units) .
4: The boy has to apply a force that is equal to the force exerted by the water. This force is the water pressure times the area of the hole. The pressure is p = d g h = 1000 kg/m^3 * 10 m/s^2 * 2 m = 20,000 Pa. The area of the hole is 1 cm^2. Since 100 cm = 1 m, we can fit 100*100 square centimeters into 1 square meter. Thus A = (1/10,000) m^2. Force = pressure * area = 20,000 Pa * (1/10,000) m^2 = 2 N. 2 N is the weight of 0.2 kg or about 1/2 pound. The child can easily stop the leak.
12: A 5 kg ball weighs 50 N (49 N to be precise). The pressure = force/area = 50 N / 1 cm^2 = 50 N / (1/10,000 m^2) = 500,000 Pa = 5 * 10^5 Pa. This is about 5 * air pressure so it is a lot of pressure. Note that 50 N/cm^2 is acceptable (but you would lose 1 point on a test because I want the answers in standard units) .
Extra Credit: Chapter 11, problem 4:
The drop of oil will still have the same volume whether it is a 0.001
milliliter droplet or a thin film covering an area of 1 square meter.
In the first case, it has a volume of 10^(-9) m^3. In the second
case, you need to multiply length * width * thickness to get the volume.
We know that length * width = 1 m^2 so that the thickness must be
10^(-9) m (or 1 nanometer) in order to get the correctr volume. This
implies that one molecule is one nanometer in diameter.