[جنون الفزياء]

1. 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.


Measurement
Section 1.3 Density and Atomic Mass
2. 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.
3. 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?
4. 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?
5. What mass of a material with density & is required to make
a hollow spherical shell having inner radius r 1 and outer
radius r 2?
6. 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.
7. 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.
8. The paragraph preceding Example 1.1 in the text
mentions that the atomic mass of aluminum is
27.0u $ 27.0 ! 1.66 ! 10"27 kg. Example 1.1 says that
27.0 g of aluminum contains 6.02 ! 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 contains 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 units 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.
9. 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.
10. A small cube of iron is observed under a microscope. The
edge of the cube is 5.00 ! 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.
11. A structural I beam is made of steel. A view of its crosssection
and its dimensions are shown in Figure P1.11. The
density of the steel is 7.56 ! 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?
15.0 cm
1.00 cm
1.00 cm
36.0 cm
Figure P1.11
12. 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 ! 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?
Section 1.4 Dimensional Analysis
The position of a particle moving under uniform acceleration
is some function of time and the acceleration. Suppose
we write this position s $ ka mt n, where k is a dimensionless
constant. Show by dimensional analysis that this expression
is satisfied if m $ 1 and n $ 2. Can this analysis give the
value of k?
14. Figure P1.14 shows a frustrum of a cone. Of the following
mensuration (geometrical) expressions, which describes
(a) the total circumference of the flat circular
faces (b) the volume (c) the area of the curved surface?
(i) #(r 1 ' r 2)[h2 ' (r 1 " r 2)2]1/2 (ii) 2#(r 1 ' r 2)
(iii) #h(r 1
2 ' r 1r 2 ' r 2
2).
13.