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Question & Answer:

  • A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure P1.1a. The atoms reside at the corners of cubes of side L = 0.200nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal, as shown in Figure P1.1b. Calculate the spacing d between two adjacent atomic planes that separate when the crystal cleaves.
  • Use information on the endpapers of this book to calculate the average density of the Earth. Where does the value fit among those listed in Tables 1.5 and 14.1? Look up the density of a typical surface rock like granite in another source and compare the density of the Earth to it.
  • The standard kilogram is a platinum–iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?
  • A major motor company displays a die-cast model of its first automobile, made from 9.35 kg of iron. To celebrate its hundredth year in business, a worker will recast the model in gold from the original dies. What mass of gold is needed to make the new model?
  • What mass of a material with density P is required to make a hollow spherical shell having inner radius r 1 and outer radius r 2?

  • Two spheres are cut from a certain uniform rock. One has radius 4.50 cm. The mass of the other is five times greater. Find its radius.
  • Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively.
  • The paragraph preceding Example 1.1 in the text mentions that the atomic mass of aluminum is 27.0u = 27.0 x 1.66 x 10-27 kg. Example 1.1 says that 27.0u g of aluminum contains 6.02 x 1023 atoms. (a) Prove that each one of these two statements implies the other. (b) What If? What if it’s not aluminum? Let M represent the numerical value of the mass of one atom of any chemical element in atomic mass units. Prove that M grams of the substance contain a particular number of atoms, the same number for all elements. Calculate this number precisely from the value for u quoted in the text. The number of atoms in M grams of an element is called Avogadro’s number NA. The idea can be extended: Avogadro’s number of molecules of a chemical compound has a mass of M grams, where M atomic mass unit is the mass of one molecule. Avogadro’s number of atoms or molecules is called one mole, symbolized as 1 mol. A periodic table of the elements, as in Appendix C, and the chemical formula for a compound contain enough information to find the molar mass of the compound. (c) Calculate the mass of one mole of water, H2O. (d) Find the molar mass of CO2-
  • On your wedding day your lover gives you a gold ring of mass 3.80 g. Fifty years later its mass is 3.35 g. On the average, how many atoms were abraded from the ring during each second of your marriage? The atomic mass of gold is 197 u.
  • A small cube of iron is observed under a microscope. The edge of the cube is 5.00 x 10-6 cm long find (a) The mass of the cube and (b) The number of iron atoms in the cube. The atomic mass of iron is 55.9 u, and its density is 7.86 g/cm3.
  • A structural I beam is made of steel. A view of its cross-section and its dimensions are shown in Figure P1.11. The density of the steel is 7.56 x 103 kg/m3 (a) What is the mass of a section 1.50 m long? (b) Assume that the atoms are predominantly iron, with atomic mass 55.9 u. How many atoms are in this section?
  • A child at the beach digs a hole in the sand and uses a pail to fill it with water having a mass of 1.20 kg. The mass of one molecule of water is 18.0 u.
    (a) Find the number of water molecules in this pail of water.
    (b) Suppose the quantity of water on Earth is constant at 1.32 x 1021 kg. How many of the water molecules in this pail of water are likely to have been in an equal quantity of water that once filled one particular claw print left by a Tyrannosaur hunting on a similar beach?
  • The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position s = kamt n, where k is a dimensionless constant. Show by dimensional analysis that this expression satisfied if m = 1 and n = 2. Can this analysis give the value of k?
  • Figure P1.14 shows a frustum of a cone. Of the following mensuration (geometrical) expressions, this describes (a) The total circumference of the flat circular faces (b) The volume (c) The area of the curved surface? (i) π (r 1 + r 2) [h2 + (r 1 - r 2)2]1/2 (ii) 2π (r 1 + r 2) (iii) πh (r 12 + r 1r 2 + r 22).
  • Which of the following equations are dimensionally correct? (a) vf = vi' + ax (b) y = (2 m) cos (kx), where k = 2 m-1.
  • (a) A fundamental law of motion states that the acceleration of an object is directly proportional to the resultant force exerted on the object and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (b) The Newton is the SI unit of force. According to the results for (a), how can you express a force having units of Newton’s using the fundamental Units of mass, length, and time?
  • Newton’s law of universal gravitation is represented by F = GMm / r2 Here F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg•m/s2.What are the SI units of the proportionality constant G?
  • A worker is to paint the walls of a square room 8.00 ft high and 12.0 ft along each side. What surface area in square meters must she cover?
  • Suppose your hair grows at the rate 1/32 in. per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1nm, your answer suggests how rapidly layers of atoms are assembled in this protein synthesis.
  • The volume of a wallet is 8.50 in3 Convert this value to m3, Using the definition 1 in. = 2.54 cm