Physical Chemistry , 1st ed.

several phenomena could not be explained by the scientific thinking of the

1800s. Most of these phenomena were based on the properties of atoms that

were only then being examined directly. These phenomena are described here

because they will be considered later in light of new theories such as quantum

mechanics. Of course, since most matter is ultimately studied using light, a

proper understanding of the nature of light is necessary. This understanding

began to change dramatically with Planck and his quantum theory of black-

bodies. Proposed in 1900, quantum theory opened a new age of science in

which new ideas began replacing the old ones—not because of lack of appli-

cation (classical mechanics is still a very useful topic), but because these old

ideas lacked the subtlety to explain newly observed phenomena properly.

Einstein’s application of quantum theory to light in 1905 was a crucial step.

Finally, Bohr’s theory of hydrogen, de Broglie’s matter waves, and other new

ideas set the stage for the introduction of modern quantum mechanics.

9.2 Laws of Motion

Throughout the Middle Ages and the Renaissance, natural philosophers stud-

ied the world around them and tried to understand the universe. Foremost

among these natural philosophers was Isaac Newton (Figure 9.1), who in the

late 1600s and early 1700s deduced several statements that summarize the mo-

tion of bodies of matter. We know them as Newton’s laws of motion.

Briefly, they are:

• The first law of motion:An object at rest tends to stay at rest, and an ob-
  ject in motion tends to stay in motion, as long as no unbalanced force
  acts on that object. (This is sometimes known as the law of inertia.)


• The second law of motion:If an unbalanced force acts on an object, that
  object will accelerate in the direction of the force, and the amount of ac-
  celeration will be inversely proportional to the mass of the object and di-
  rectly proportional to the force.


• The third law of motion:For every action, there is an equal and opposite
  reaction.
  Newton’s second law should be considered more closely, since it is perhaps
  the most familiar of the laws. Force,F, is a vectorquantity, having magnitude
  and direction. For a single object of mass m, Newton’s second law is usually ex-
  pressed in the form*
  Fma (9.1)
  where the boldfaced variables are vector quantities. Note that the acceleration
  ais also a vector, since it too has magnitude and direction. Typical units
  for mass, acceleration, and force are kg, m/s^2 , and newton (where 1 N 
  1 kgm/s^2 ). Equation 9.1 assumes that mass is constant.
  Equation 9.1 can be written in a different way using the symbolism of cal-
  culus. Acceleration is the change of the velocity vector with respect to time, or
  dv/dt. But velocity vis the change in position with respect to time. If we rep-
  resent the position by its one-dimensional coordinate x, then we can write ac-
  celeration as the time derivative of the time derivative of position, or

a

d

dt

(^2) x
 2 (9.2)
242 CHAPTER 9 Pre-Quantum Mechanics
Figure 9.1 Sir Isaac Newton (1642–1727). In
1687, he published Principia Mathematica,in
which his three laws of motion were first stated.
They are still the most widespread way to de-
scribe the motion of objects. Knighted in 1705,
Newton received this honor not for his scientific
achievements, as is usually assumed, but for his
political activities.
*Its most general form is Fdp/dtdmv/dt, but the form in equation 9.1 is probably
the most common way to express Newton’s second law.
© CORBIS-Bettmann