Download The Hydrogen Atom

Lecture 24
The Hydrogen Atom
Chapter 28.4  28.9
Outline
• Atomic Spectra
• The Bohr Model
• Modifications to the Bohr Model
Summary of Early Atomic Models
The Thomson Model
Description: Electrons are embedded in a wide
positively charged area, like raisins in a cookie.
Problem: Does not agree with the Rutherford particles experiment.
The Rutherford Model
Description: Miniature Solar system with electrons
orbiting the nucleus at any distance.
Problem: Electrons experience acceleration and
should lose energy by radiating photons and
eventually fall onto the nucleus.
Three Types of Spectra
When a material object is heated, electrons in the
atoms absorb energy from the current and emit colored
light, which can be dispersed into a spectrum.
At high densities, the emission is continuous with no
peaks within a short wavelength range.
At lower densities, we will see series of bright lines,
some of which are more intense.
The color of the most intense lines gives the excited
gas its color (red to neon)  emission spectrum.
Three Types of Spectra
Absorption spectra occur when light from a hot
source passes through a cool gas before entering the
spectroscope.
The light source alone would give a continuous
spectrum, but atoms of the gas absorb certain
frequencies from the light.
The lines in the emission and absorption spectrum
of the same chemical element have the same
frequencies.
Frequencies in the spectrum of an element fall into
sets called spectral series.
The Bohr Model
In 1913 Niels Bohr proposed a theory of the
hydrogen atom that could account for its stability
and for the frequencies of its spectral lines.
• An electron can circle the nucleus without losing
energy only in certain specific orbits.
• The energy of the electron depends on which
orbit it is in.

Atomic electrons can have only certain particular
energies.
The Bohr Model
An electron in the innermost orbit has the least energy.
The larger the orbit, the more the electron has energy.
The orbits are identified by a quantum number, n.
Each orbit has an energy level En = 13.6/n2 eV.
An electron can absorb only those photons whose
energy permit it to jump from one orbit (ni) to another,
farther out (nf).
When an electron jumps to an orbit, closer to the
nucleus, it emits a photon of a wavelength .
1
1
1
RH  Rydberg constant
 = RH   
7 m1
R
=
1.097
10
H

nf2 ni2
Electron Waves and Orbits
Why does an atomic electron follow certain orbits
only?
The de Broglie wavelength of the electron is exactly
equal to the circumference of its ground state (the
innermost orbit with n=1).
If we consider the vibrations of a wire loop, we find
that their wavelengths always fit a whole number of
times into the loop’s circumference.
An electron can circle a nucleus only in orbits that
contain an integral number of de Broglie wavelengths.
Quantum Theory of the Atom
The Bohr’s model has some severe limitations.
It correctly predicts the spectral series for
hydrogen, but fails predicting the same for atoms
with 2 or more electrons.
A more general approach was developed in 1925/6
by Erwin Schrodinger, Werner Heisenberg, and
others, and is called quantum mechanics.
Classical versus Quantum Mechanics
Classical mechanics takes such quantities as position,
mass, velocity, and acceleration for granted.
Quantum mechanics uses the uncertainty principle
instead and explores probabilities.
It deals only with quantities that can actually be
measured.
The measurable quantities are mass of the electron, its
electric charge, frequencies of spectral lines, etc.
But we cannot measure the precise diameter of an
electron’s orbit.
Quantum mechanics includes Newtonian mechanics as
a special case.
Quantum Numbers
In the quantum theory of atom, an electron has no
fixed orbit but is free to move about 3 dimensions.
It circulates in a probability cloud and can be found
where the cloud is the most dense.
Three quantum numbers determine the size and
shape of the probability cloud of an atomic electron.
n  the principal quantum number
l  the orbital quantum number
ml  the magnetic quantum number
The 4th, spin quantum number (ms) determines the
maximum number of electrons allowed on an orbit.
Summary
The Bohr model correctly explained properties of
only hydrogen atoms.
Quantum theory of atom is a probabilistic
approach, which enlarges applications of the
classical mechanics.
Quantum mechanics shows that four quantum
numbers are needed to specify the physical state
of each atomic electron.