Solutions to 1996 Questions

·

Solution to December 1996 Puzzle of the Month

The question was: Why does ice float on water ? Aren't molecules supposed to get closer together as they cool and lose energy?.

Solution: As water molecules cool they do get closer together, generally making cold water more dense than warm water. But at 4o C, water attains its maximum density. Its density keeps decreasing,meaning that the space between molecules start to increase until the freezing point is reached. Why ? The combination of H-bonding and lossof kinetic energy allows a hexagonal pattern (though not flat) of H2O molecules to emerge. A given volume of ice, with its repeating lawn-chairshaped hexagons, has less water molecules than an equal volume of liquid water. The latter can therefore support the weight of the former. The 0 to <4 degree range represents a kind of transition state where the molecules are slowed down enough for part of the pattern to emerge, so that such water is not as dense as it is at 4oC.

### Solution to November 1996 Puzzle of the Month

The question was: How many water molecules fit into the eye of a needle ?

Solution: Assuming that the eye of a needle is 0.1 by 0.1 by 0.2 cm, we have a volume of 0.002 cm3. Water's density is about 1 g/cm3. Dividing by its molar mass of 18 g/mole and multiplying by the number of molecules per mole ( 6.02 X 1023), we obtain, paying attentiion to significant figures, 7 X 1019molecules.If we had that number of pennies we could give each of the 6 billion people on earth over 100 million dollars.

### Solution to October Puzzle of the Month

The question was: You're on a hot air balloon that is ascending at a constant velocity. As you rise past the nest of an eagle you suddenly drop your keys overboard. Will the eagle in the nest see your keys go up momentarily ? If not, why not? If so, for how long?

Solution:The keys will be seen going up, for how long depends on the initial upward velocity,v, of the balloon. Since displacement = 0 (the keys go up and then momentarily back to the eagle's eye-level) and if gravity = 10 m/s2, then 0 = vt - 5t2. Solving for t, we realize the keys will be above the eagle for t = v/5 seconds.

### Solution to September Puzzle of the Month

The question was: A man walks 12 m east and then 5.0 m south in 13 seconds. What is his average velocity ?

Solution: Velocity is displacement over time. Although the distance covered in 13 seconds was 15 m , the displacement from the original point was 13 m (Pythagorean Theorem). Thus, the avg. velocity = 1.0 m/s.

### Solution To August Puzzle of the Month

The question was: A cyclotron can be used to bombard an element with a hydrogen-2 nucleus. This isotope consists of a neutron and a proton, but the pair is split as it approaches the nucleus of the target element. The undeviated neutron can then be absorbed by whatever element is to be attacked, and the neutron will be converted into a proton and a beta particle.

In other words, an element attacked by a hydrogen-2 can go up in atomic number.

An American physicist, Ernest Lawrence, made molybdenum radioactive by bombarding it with hydrogen-2. When another group of scientists analyzed the sample, they found several known elements included among the mixture of products, but none of the known elements were radioactive. If, however, manganese or rhenium (two elements chemically similar to each other; see their position in the periodic table) were added to the mixture, the lot came back out radioactive when isolated. What was going on?

Solution: Molybdenum is atomic number 42. Through neutron capture and the subsequent increase in atomic number, some of the nuclei acquire an atomic number of 43, a radioactive element (technetium) unknown to Lawrence. The other group of scientists was isolating byproducts, all of which were known elements, none of which were radioactive. Now the radioactive culprit with atomic number 43 lies in between manganese and rhenium on the periodic table. Since 43's chemical properties are similar to those of its relatives, it tagged along with manganese or rhenium when either element was separated again from the mixture. To the researchers, it seemed that either Mn or Rh had become radioactive, but in reality it was Tc that was emitting radiation.

### Solution To July Puzzle of the Month

The question was: When salt is added to water, why does it eventually disappear ?

Solution: Water is a polar molecule. This does not imply that it has relatives in Northern Canada, but it means that the oxygen atom in water has a partial negative charge which allows it to attract the positive sodium ion in salt. The hydrogen atoms in water carry a partial positive charge, allowing them to attract salt's negative chloride ion .The attractions between water and salt are strong enough that they overcome the bonds that keep sodium chloride solid. As salt's ions come apart and find themselves trapped among water molecules, we no longer see them.

### Solution To June Puzzle of the Month

The question was: Carry out a thought-experiment involving two masses and a string to demonstrate that a heavier object in free fall cannot accelerate faster than a lighter object.

Solution: If we assume that a heavier object accelerates faster in free fall, we can think of attaching the two masses with a string. We would then assume that the heavier mass will then be slowed down by the lagging smaller mass. But if the masses are attached, then the entire system represents a larger mass which should accelerate faster. This leads to a contradiction,which implies that our original assumption is false. A heavier object in free fall cannot accelerate faster than a lighter object.

Page Maintained by E.Uva