Page 46 - Modern physical chemistry

Problems 35

trons is taken to be zero. Then one finds that Ro ranges from 1.2 fm for heavy nuclei to
1.3 fin for light nuclei.
In the approximation that equation (2.41) holds with Ro constant, the volume of a
nucleus is proportional to its mass number
4 3 4 3 ( )
VA = 31rRA = 3nRo A = const A. [2.43]

This result suggests that a nucleus consists of A particles, each occupying the volume
(413)irRo • In modem theory, these are taken to be neutrons and protons. The number of
3
protons is taken to equal the atomic number Z.
2.9 Composition of Atoms and Nuclei
Certain key experimental facts and their implications will now be summarized.
The charged particles that are easily driven out of materials by projectile particles
and by heat are electrons. Presumably they come from the outer regions of atoms in the
materials. The transparency of a substance to small projectiles shows how extensive
these regions are. Under appropriate conditions, the radii of the absorbing regions, the
nuclei, can be determined. These are small fractions of the atomic radii calculated from
the observed interatomic spacings in molecules and in crystals.
The mass to charge ratio of particles can be determined from the observed deflec-
tions in a magnetic field. The charge on the highly mobile particle, the electron, can be
determined from observations of the movements of small spheres in air in combined
electric and gravitational fields.
One can observe the movements of an atom stripped of various numbers of its elec-
trons in a mass spectrograph. It is found that the total number of electrons in an uncharged
atom equals its number in the periodic table, the atomic number Z.
The unit for atomic mass is one-twelfth the mass of the atom 12C. For other nuclides,
the integer closest to the atomic mass is called the mass number A. The volume of a
nucleus is apprOximately proportional to its mass number.

Questions
2.1 What chemical evidence do we have for the atomic theory of matter?
2.2 What evidence do we have that electrons are the agents that hold atoms together in molecules?
2.3 Define the term chemical bond.
2.4 Explain how the bond angles in small coordination structures may be determined.
2.5 How is the de Broglie equation justified?
2.6 How is a beam of particles with a definite wavevector obtained?
2.7 How can a jet of molecules produce a diffraction pattern?
2.8 How may the interatomic distances and angles be determined?
2.9 Define the intenSity in a beam.
2.10 How is this intensity measured?
2.11 In what units does electromagnetic radiation interact with matter?
2.12 Define the cross section of an atom or molecule.
2.13 Show how the intensity of a beam decreases on passing through a target.
2.14 What is the continuum apprOximation?
2.15 Cite the evidence for the nuclear atom.
2.16 What is the conventional unit for atomic and molecular masses?
Problems

2.1 Molecule ABa has a trigonal pyramid structure. Show that for the dipole moment to be
directed perpendicular to the base, the B's must lie at the corners of an equilateral triangle.