Transcript probability = ψ 2

Hψ = E ψ
Hamiltonian for the H atom
The wave function is usually represented by
ψ
2
The electron density is given by ψ
probability
= ψ2
Electron
Density
Radius r
Wave function
0.5
ψ
0.4
0.3
0.2
0.1
1 2 3 4 5
The wave function and probability distribution as functions of r for
the n = 1 level of the H atom. The functions and the radius r are
in atomic units
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html
Wave function
0.5
0.3
Electron density
ψ
0.4
ψ2
0.2
0.3
0.2
0.1
0.1
1 2 3 4 5
1
2
3
4
The wave function and probability distribution as functions of r for
the n = 1 level of the H atom. The functions and the radius r are
in atomic units
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html
probability = ψ2
2.0
1.0
Radial Wave function
Radial Distribution Function
0.0
0.0
1.0
2.0
3.0
r in atomic units – Bohr Radii = 1 (ca 0.5Ǻ)
4.0
5.0
4πr2ψ2
4πr2ψ2
4πr2ψ2
32
5 4 3 2 1 0 1 2 3 4 5
%
32 74
%
5 4 3 2 1 0 1 2 3 4 5
32 74 93
%
5 4 3 2 1 0 1 2 3 4 5
32 74 93 99 %
5 4 3 2 1 0 1 2 3 4 5
Wave function
Electron density
ψ
ψ2
The wave function and probability distribution as
functions of r for the n = 1 level of the H atom. The
functions and the radius r are in atomic units
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html
Radial
Distribution
Function
2.0
1.0
0.0
0.0
1.0
2.0
3.0
4.0
5.0
Hydrogen. The two electrons in the hydrogen molecule may
both be accommodated in the 1sg orbital if their spins are
paired and the molecular orbital configuration for H2 is 1sg2.
Since the 1sg orbital is the only occupied orbital in the ground
state of H2, the density distribution shown previously in Fig. 62 for H2 is also the density distribution for the 1sg orbital when
occupied by two electrons. The remarks made previously
regarding the binding of the nuclei in H2 by the molecular
charge distribution apply directly to the properties of the 1sg
charge density. Because it concentrates charge in the binding
region and exerts an attractive force on the nuclei the 1sg
orbital is classified as a bonding orbital.
http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html
Hydrogen. II
Excited electronic configurations for molecules may be
described and predicted with the same ease within the
framework of molecular orbital theory as are the excited
configurations of atoms in the corresponding atomic orbital
theory. For example, an electron in H2 may be excited to any
of the vacant orbitals of higher energy indicated in the energy
level diagram. The excited molecule may return to its ground
configuration with the emission of a photon. The energy of the
photon will be given approximately by the difference in the
energies of the excited orbital and the 1sg ground state orbital.
Thus molecules as well as atoms will exhibit a line spectrum.
The electronic line spectrum obtained from a molecule is,
however, complicated by the appearance of many
accompanying side bands. These have their origin in changes
in the vibrational energy of the molecule which accompany the
change in electronic energy.
The nucleus is the very dense region consisting of
nucleons (protons and neutrons) at the center of an
atom. Almost all of the mass in an atom is made up
from the protons and neutrons in the nucleus, with a
very small contribution from the orbiting electrons.
The diameter of the nucleus is in the range of 1.6 fm
(1.6 × 10−15 m) (for a proton in light hydrogen) to
about 15 fm (for the heaviest atoms, such as
uranium). These dimensions are much smaller than
the diameter of the atom itself, by a factor of about
23,000 (uranium) to about 145,000 (hydrogen).
The branch of physics concerned with studying and
understanding the atomic nucleus, including its
composition and the forces which bind it together, is
called nuclear physics.
http://tannerm.com/diatomic.htm