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March Monthly Question

Crystal Ball

Solutions to 2000 Monthly Puzzles

  • January 2000: Galilean Oddball
  • February 2000: Blind But Chem-smart
  • March 2000: Humans Or Robots On Mars?
  • April 2000: Charged Knobs
  • May 2000: Gravity for the Little Prince
  • June 2000: How a Motor Runs
  • July 2000: Ferromagnetic Mysteries
  • August 2000: Getting A Planet's Width Without Getting There
  • September 2000: Limewater Without Limes
  • October 2000: More Protons Don't Always Make an Atom Bigger
  • November 2000: Solutions On Paper May Be Deceiving
  • December 2000: A Ball of Gold
  • Solutions to 2009 Questions
  • Solutions to 2007 Questions
  • Solutions to 2006 Questions
  • Solutions to 2005 Questions
  • Solutions to 2004 Questions
  • Solutions to 2003 Questions
  • Solutions to 2002 Questions
  • Solutions to 2001 Questions
  • Solutions to 2000 Questions
  • Solutions to 1999 Questions
  • Solutions to 1998 Questions
  • Solutions to 1997 Questions
  • Solutions to 1996 Questions
  • Questions Sorted By Topic

  • Solution to January 2000 Puzzle of the Month

    The question was:

    One of the four Galilean moons of Jupiter is an oddball, in the sense that it is not geologically differentiated like the other three. Which one is it?

    Solution:

    Callisto is the moon we're looking for. The other three Galilean satellites are believed to have an iron core surrounded by a rocky mantle ( Europa and Ganymede) or a highly molten mantle, in the case of volcanic Io. Callisto, however, has a mixed ice-rock interior, extending from the core to what may be an ocean that is responsible for an electrically conducting layer that weakly perturbs Jupiter's magnetic field. (see Scientific American, Feb,2000) .


    Solution to February 2000 Puzzle of the Month

    The question was:

    A blind student has to tell a base from an acid. Neither container is labeled in braille, and he cannot touch or taste any of the two substances because they may be toxic, even upon dilution. All the other chemicals are identified in braille. How does he eventually figure out which is which?

    Solution:
    There are at least two ways by which a blind student who know his chemistry can differentiate between the two. Although he cannot touch or taste either, he can feel the container. Since the other acids and bases in the supply room are labeled in braille, he can add a base to each unknown. When the acid comes into contact with the base, heat will be released and will warm the beaker. Alternatively, he can add magnesium to both unknowns. Only the acid will produce a fizzing sound, as hydrogen is released from the acid.


    Solution to March 2000 Puzzle of the Month

    The question was:

    What scientific advantages are there to putting humans on Mars instead of of robots?

    Solution:

    One of the main reasons NASA is interested in Mars is that there may be microscopic life on that planet or it may have harboured such forms at one point. If life exists, it is unlikely to be found on its surface where high levels of ultraviolet rays and atmospheric traces of hydrogen peroxide would quickly destroy organic molecules. Thus samples have to be taken from deep underground, and with present technology robots are not up to the task of drilling.

    For a more elaborate discussion, see " Scientific American: March 2000, Why Go To Mars? "


    Solution to April 2000 Puzzle of the Month

    The question was:

    Here's an interesting question from a student: when someone gets a shock from touching a metallic door knob on a dry day, does the metal actually form positive ions as it loses electrons to an electron-deficient body?

    Solution:

    Although the knob does acquire a positive charge as some electrons flow out of the sea of electrons that surrounds atoms of iron, there are few electrons actually lost relative to the total number of iron atoms present. Otherwise there would be negative ions quickly attracted to the positive iron, and that would constitute rust.


    Solution to May 2000 Puzzle of the Month

    The question was:

    What is the surface gravity of the average asteroid?

    Solution:

    Ceres is the largest of the asteroids with a diameter of about 913 km. Mass is proportional to its volume which in turn is proportional to the cube of its radius. Surface gravity is proportional to the mass of a planetary body and inversely proprtional to the square of its radius. Assuming a similar density between the asteroid and that of the earth, the surface gravity becomes simply the fraction of the earth's radius*its gravity = (913/6380)*9.8=1.4. But Ceres is only 0.42 times as dense as the earth, so its gravity becomes 1.4*0.42=0.58 or about 1/17th that of the earth. The majority of the asteroids, however, are a lot smaller than Ceres, in fact smaller than 1 km in diameter. That would make gravity < 1/6380 that of the earth, without diminishing it with density-considerations.


    Solution to June 2000 Puzzle of the Month

    The question was:

    How does an electric motor run?

    Solution:

    A motor consists of an armature ( turning loop of current carrying metal) in a fixed magnetic field(from a permanent magnet). Depending on the direction of the current, the magnetic field induced by this current in the armature reinforces the external magnetic field above or below the armature. Since the field is also weakened on the opposite side, there is a net force that will cause the armature to turn. In order for the turn to be complete, the direction of the current and hence the direction of the force must change. This is made possible by a gap in the ring holding the ends of the loop, When a current-carrying brush skips over the gap, the flow of electrons through the loop changes direction.


    Solution to July 2000 Puzzle of the Month

    The question was:

    Why are only certain elements ferromagnetic?

    Solution:

    A ferromagnetic element can be picked up by a magnet and can, with impurities and an electromagnet, be converted into a permanent magnet. Magnetism is a property of matter itself: when an electron spins around the nucleus, it creates a magnetic field. If an electron from the same orbital or from an outer orbital of an adjacent atom spins in the opposite direction, then the magnetic fields cancel out. Although many metals have unpaired electrons, most are not magnetic for the reason just mentioned. In a ferromagnetic substance, instead of cancelling, the spins are coupled into a parallel alignment over thousands of atoms. This constitutes a domain. Different domains don't act in unison when a ferromagnetic material is not in a magnetic field, but the domains get aligned when a magnet attracts them, and for that reason a paper clip stuck to a magnet will pick up another paper clip. But why do domains form in Co, Fe, Ni, Sm, Nd ( also in Gd, Tb and Dy but only at low temperatures)? These elements are the only ones that have shielded and unpaired d and f orbital electrons that cannot pair with unpaired electrons from neighboring atoms.
    Reference: Shriver, Inorganic Chemistry. Freeman.(1990)


    Solution to August 2000 Puzzle of the Month

    The question was:

    How were the diameters of planets measured before space travel?

    Solution:

    The diameter of a planet can be measured if its distance from the earth is known. It's based on the idea that the farther an object is, the smaller it appears. For instance, a book at arm's length appears to be the size of a hand. But across the room it seems as big as a fingernail. The apparent width of a planet, a, is measured in "seconds of arc" (one second of an arc is 1/3600 of a degree), and its actual diameter, d, can be determined by the formula:
    d = aD/206 265, where D = distance between planet and earth.
    How did astronomers get D?
    Well, first they used right-triangle geometry (basic trigonometry) to figure out the relative distances between the planets and the sun. They waited for Venus to appear as a half-moon, and measured the angle between Venus and the sun. At that point in its orbit, Venus is the 90 degree vertex. By measuring the other angle you can figure out the ratio of Venus- sun distance to that of the earth-sun distance. They did the same thing for Mercury, and something slightly more complicated for outer planets like Mars , Jupiter and Saturn and obtained very accurate values even by today's standards.
    When Cassini came along in the late 1600's, he calculated the actual distance to Mars using parallax. This is based on the idea that nearby objects seem to move more against their background if you change your point of view. Hold your finger in front of your face and stare at it with one eye shut. Then without moving your finger, close your other eye and open the closed one. The finger seems to move to the left or to the right, depending on which eye was opened first. Cassini two different seasons (the earth is at two different positions), and he measured Mars' apparent movement against the background of the stars. This allowed him to get an actual distance in miles. Since it was known from trigonometry that it was 1.5 times as far from the sun as earth was, they just had to divide that distance by 1.5 and realized that the earth is 93 000 000 miles from the sun.
    Reference: Universe. Kaufmann, William J. Freeman. 1985


    Solution to September 2000 Puzzle of the Month

    The question was:

    How would you make limewater if the only chemicals you had were a piece of calcium and water?

    Solution:

    If the calcium is added to water, hydrogen gas will be released but Ca(OH)2will also form. Most of it will precipitate, but the rest will stay in solution as limewater. The mixture can then be filtered, and if you blow into the filtrate, CO2 will react with the limewater. The solution will get cloudy as calcium carbonate forms and precipitates from the reaction. By the way the limewater referred to in this solution has nothing to do with lime fruit. Lime (CaO) is alkaline and certainly not drinkable. CaO +H2O= Ca(OH)2


    Solution to October 2000 Puzzle of the Month

    The question was:

    Boron has 5 protons and 5 electrons and yet it is a bigger atom than carbon, which has 6 protons and 6 electrons. How can that be?

    Solution:

    Usually it is the number of energy levels(shells) that determine the size of the atom. For that reason, an aluminum atom is bigger than boron. But both carbon and boron have their outermost electrons in the second shell. The extra proton in carbon's nucleus causes a greater attraction, reducing the distance between the nucleus and the valence electrons.


    Solution to November 2000 Puzzle of the Month

    The question was:

    Can you come up with three different dot structures for C3H8O? Are there more than three different ones?

    Solution:
    • The first dot structure is equivalent to CH3(CH-OH)CH3. This is isopropyl alcohol. (rubbing alcohol)
    • The second one is equivalent to CH3CH2O CH3. This is ethyl methyl ether.
    • The third one is CH3CH2OH. This is n-propyl alcohol.

    These 3 are the only possible answers. As an alternative to the second solution, if you place the methyl group first, you are really describing the same molecule even though it looks different on paper.


    Solution to December 2000 Puzzle of the Month

    The question was:

    1. How much is a 12 inch(diameter) globe of solid gold worth if gold sells for $14 per gram?

    and
      Balance the following: H2O + Cr+3 +Cl2 --> Cr2O7-2 + Cl-1 + H+1
    Solution:

    Part 1

    To answer the first part of the question, you need the density of pure gold = 19.3 g/cm3. 12 inches = 2.54 cm/in*12in = 30.48 cm, so the radius = 15.24 cm.

    Its volume =(4/3)(3.1415)*(15.24)3=14826.2 cm3

    The mass of such a globe= density*volume=14826.2 cm3*19.3=286146 g

    At $14 per gram = about 4 million dollars!


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    Created: 7/4/96; Updated:15/02/2001