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Solutions to 1997 Monthly Puzzles

  • December 1997: The Strong Force
  • November 1997: Colour of Clouds
  • October 1997: Burnt Toast
  • September 1997: Classifying Garden Plants
  • August 1997: Alkali Metals
  • July 1997: Entropy of Rubber Bands
  • June 1997: Lenticular Clouds
  • May 1997: Uranus
  • April 1997: Magnets
  • March 1997: Anthocyanins II
  • February 1997: Anthocyanins I
  • January 1997: Big Bang
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    Solution to December 1997 Puzzle of the Month

    The question was:

    If the nucleus of an atom consists of neutral and positive particles, why don`t the positive particles (protons) repel one another ?

    Solution:

    Protons, are kept together by a strong force mediated by gluons. These particles actually operate between quarks ; the exchange process binds them just as it does with the weak force, and since quarks make up protons and neutrons, the latter stick together.
    Gluons can only be exchanged over a small distance, acting over distances of 10-15m or less, about 10000 times smaller than the smallest atom, hydrogen, and thus limiting the range of the strong force . When charged atoms of similar charges approach one another, the distance separating them is far greater than 10-15m. As a result, they repel electromagnetically. But quarks are much closer together, allowing gluons to do their thing.
    In 1935, the Japanese physicist, Hideki Yukawa, first proposed the existence of a particle responsible for the strong force. The discovery of the pi meson confirmed his hypothesis and won him the Nobel Prize in 1949. But the existence of quarks was only confirmed about 20 years later by Taylor, Friedmman and Kendall, who fired high energy electrons from a linear accelerator at protons and neutrons. Strangely, electrons were deflected at large angles. Sixty years earlier, Rutherford had obtained similar deflection angles upon firing helium nuclei at gold foil. The trio's results suggested that neither the proton nor the neutron was a solid sphere. Two up quarks and a down quark of charge +2/3 and -1/3, respectively, make up the proton, and two downs and an up make up a neutron.


    Solution to November 1997 Puzzle of the Month

    The question was:

    On a fair day, clouds are white. On an overcast day, they`re grey. How come?

    Solution: Clouds are white because the small water droplets reflect all wavelengths of light, which recombine to produce white. On an overcast day, clouds are thicker. If viewed from above, say from an airplane, they still appear white. But because some of the reflected light never makes it to the surface, they appear grey to an observer on the ground.


    Solution to October 1997 Puzzle of the Month

    The question was:

    One day, Squigley toasted two pieces of sliced bread and they popped out on the whitish side, just barely brown. The next morning she sliced some Italian bread that had been lying around for two days. After sitting in the same toaster for the same amount of time and at the same temperature setting, the bread popped out slightly burnt. What was going on?

    Solution:The stale bread had less moisture, which caused its temperature to increase to an unfavourable point, even though it had absorbed the same amount of heat as the sliced bread.


    Solution to September 1997 Puzzle of the Month

    The question was:

    If you're lucky enough to have a summer garden, use as many senses as possible to examine the following plants: tomato, parsley, basil, mint and a carrot. Into how many groups would you classify them ?

    Solution: They should be placed into three separate groups: tomatoes by themselves; basil with mint; and carrots with parsley. Tomatoes, basil and mint all have strongly scented leaves, but unlike mint and basil, tomato stems do not have square cross sections ( feel them if you're nearsighted! ) and they have lobed compound leaves instead of simple, opposite leaves. In addition tomatoes have star-shaped flowers with fused petals. Mint and basil both have flowers forming a prominent lower lip.

    Carrots and parsley both form an umbel, an umbrella-shaped aggregate of small flowers characteristic of their family.


    Solution to August 1997 Puzzle of the Month

    The question was: The first ionization energy for Li, lithium, is 520 kJ/mole. But for K, potassium, it is only 419 kJ/mole, meaning that it is easier to remove a valence electron from K. The standard reduction potential at 298 K for lithium is 3.05 V but only 2.92 V for potassium, meaning that in an aqueous solution lithium is a better reducing agent ( better at losing an electron) than potassium. Yet add potassium to water and it reacts a lot more violently than lithium. How do you reconcile these apparent inconsistencies?

    Solution: Ionization energies are measured for gases. But in water, the loss of an electron from Li is more likely than one from K . This is because Li+1 is smaller, thus it is more strongly attracted to water molecules. Nonetheless, potassium has a lower melting point, so when it comes into contact with water the heat released from the initial reaction melts more metal, increasing its surface area and the rate of the reaction.


    Solution to July 1997 Puzzle of the Month

    The question was: Stretch a rubber band and determine whether the change is exothermic. From this, can you conclude whether stretched rubber's molecules are more orderly than unstretched ones?

    Solution: By holding a stretched rubber band against your lips you should feel its warmth: stretching is exothermic. (Depending on the type of rubber band, the effect may not be noticeable.)Yet rubber bands don't stretch on their own; hence DG is (+). Since DG = DH - TDS, DS must be negative, meaning that stretched rubber's molecules are more orderly than unstretched ones. As the long molecules remain intact, there are less possibilities for its conformations in an outstreched mode. When the ends of the molecules are brought together, various 3D-conformations are possible, giving the unstretched molecules a higher entropy.Similarly, a contracted muscle has a higher entropy than a relaxed one.


    Solution to June 1997 Puzzle of the Month

    The question was: A not so prominent newspaper reports that a huge flying saucer was seen over a mountainous area in Washington state. Unlike other stories this one is apparently not pure fabrication, just a misinterpretation by dozens of people. What could they have seen ?

    Solution: Occasionally, lenticular (lens -shaped) altocumulus clouds form over mountainous areas. Rarely, with the right airflow, such clouds will acquire a remarkable symmetry, and they look just like "flying saucers."

    from http://www.islandnet.com/~see/weather/graphics/photos0910/Wea00008.jpg


    Solution to May 1997 Puzzle of the Month

    The question was:Uranus's axis of rotation lies more or less in the plane of the planet's orbit. Based on this, how many seasons do you expect it to have?

    Solution: Four.The planet's north and south poles alternately point toward or away from the sun.Then just like on earth, there is a spring and fall in between the extreme seasons.


    Solution to April 1997 Puzzle of the Month

    The question was: One of the magnets in our lab had the brand name Alnico. Is there any connection between the name and the composition of the magnet ?

    Solution: Nickel (Ni) and cobalt (Co) are two of three ferromagnetic substances.( The other being Fe, iron.) Like all ferromagnetic substances, if placed in their pure form in a magnetic field, Co and Ni will not become permanent magnets. As soon as the current is turned off, the domains ( the groups of atoms that act as miniature magnets) will scramble again, and the material will stop acting as a magnet. Maybe the aluminum (Al) is purposely added as an impurity to prevent the domains from moving around after their magnetic dipoles have been aligned.


    Solution to March 1997 Puzzle of the Month

     

    The question was: This one's related to the previous month's question. Suppose you took some denatured ethanol (95%) and added purple cabbage to it. After a few minutes, the alcohol takes on a violet hue. In hot water, however, no pun intended, a blue colour is released. Purple cabbage contains anthocyanins that act as indicators, but both water and ethanol have the same pH. What's going on? Would the alcohol turn blue if it was also hot? Try it!

    Solution: Hey! You have to try it first! You may be surprised. Then e-mail me your answer at euva@retired.ca


    Solution to February 1997 Puzzle of the Month

     

    The question was: A Canadian friend gives you some red maple leaves. You boil them in water, and although their colour fades, the water turns brown, not red. If you add lemon juice, the water turns pink. Add a bit of baking soda and the pink colour disappears again. A thin slice under the microscope reveals little red compartments within each cell.

    What's going on?

    Solution: The little red compartments in the cells are vacuoles which store anthocyanins and acid. In the presence of acids, most anthocyanins turn red. But boiling ruptures the vacuoles, and their contents are neutralized by the alkaline cytoplasm of the cell. In a neutral solution, anthocyanins change colour, which explains why the colour of the boiling water is not pink. Reacidifying the solution with lemon, restores the red colour. Baking soda, however, is alkaline just like the cytoplasm. Once again the pink or reddish colour fades, simulating the first neutralization. For more on anthocyanins, check out this neat link from UBC.


    Solution to January 1997 Puzzle of the Month

    The question was: Imagine an early universe with nothing but free protons and neutrons, in fact seven times as many protons as neutrons. Assume that each neutron fuses with a proton to make 2H. Then assume that all the 2H formed pair off to make 4He.

    What then is the mass % of 4He in the universe?

    Solution: The easiest thing is to start off with an example of 28 protons. If the ratio is 7:1, then there are 4 neutrons. After the latter fuse with protons we're left with four 2H's and 24 free protons. Finally two heliums will form from the four deuteriums. Each helium has a mass of 4, so

    % He = 2(4)/[2(4) + 24] = 25


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