Lecture 24 The Hydrogen Atom

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Lecture 24The Hydrogen Atom
Chapter 28.4 ? 28.9
Outline

• Atomic Spectra
• The Bohr Model
• Modifications to the Bohr Model

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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.
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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.
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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.
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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.

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Atomic electrons can have only certain particular
energies.
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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 ? ? ? ?
nf2 ni2
RH ? Rydberg constant RH 1.097 107 m?1
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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 n1).
If we consider the vibrations of a wire loop, we
find that their wavelengths always fit a whole
number of times into the loops circumference.
An electron can circle a nucleus only in orbits
that contain an integral number of de Broglie
wavelengths.
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Quantum Theory of the Atom
The Bohrs 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.
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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 electrons orbit.
Quantum mechanics includes Newtonian mechanics as
a special case.
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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.
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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.