Transcript Astronomy 1010 - The University of Toledo

Lecture 16
The Hydrogen Atom.
Quantum Theory of Atom.
• Atomic Spectra
• The Bohr Model of the Atom
• Quantum Theory of Atom
Atomic Spectra
When an electric current is passed through a gas, electrons
in the gas atoms absorb energy from the current.
The excited this way gas emits colored light.
If we disperse the emitted light into different frequencies,
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).
This is an emission spectrum.
Absorption 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.
It was shown that 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.
Bohr proposed than 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.
Thus Bohr suggested that 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 corresponds to an energy level of the atom.
An electron can absorb only those photons whose energy
will permit it to jump from orbit to another, farther out.
When an electron jumps from an orbit to another one,
closer to the nucleus, it emits a photon.
The difference in energy between the 2 orbits is hf, where
f is the frequency of the emitted or absorbed photon.
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.
Thus, an electron can circle a nucleus only in orbits that
contain a whole 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 of an object as its
position, mass, velocity, and acceleration for granted.
Quantum mechanics uses the uncertainty principle instead
and explores probabilities.
It deals only with quantities which 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 that forms a certain
pattern in space 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
Exclusion Principle
The fourth quantum number is ms  spin magnetic
quantum number.
In an unexcited hydrogen atom, the electron is in its
quantum state of the lowest energy.
For more complex atoms, the exclusion principle is valid:
Only one electron can exist in a given quantum state.
Each electron in an atom must have a different set of
the 4 quantum numbers.
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.