Download Particle-like Properties of Electromagnetic Radiation

Particle-like Properties of Electromagnetic Radiation
Another important discovery which helped create the underlying principles about
the atomic structure was the phenomenon called Blackbody Radiation - the
visible glow that all solids give off when heated; (Max Planck (1900)). He found
that as the object was heat at a higher temperature, the colour (or the radiant light)
of the object changed from long (low energy) to shorter (higher energy). But
this rising trend did not continue indefinitely.
Planck continued that energy radiated by a heated object is constrained to
discrete amounts or quanta. The increase to more energized radiation is not
ramped, rather it is like stairs which are quantized.
Amount of energy , E, associated with a quanta is related to the (or )
E= h
=hc
where h = Planck s constant (6.626 x 10-34 J . s)
Therefore, the energy of one quantum of red light ( = 650 nm (or
= 4.62 x 1014 s-1) is:
E = h = (6.626 x 10 -34 J. s) x (4.62 x 1014 s-) = 3.06 x 10 -19 J
very small amount
Einstein further explained a beam of irradiation as behaving like
small particles called photons.
The light particle has a mass (m) and the relationship between m and
wavelength is
m = E = hc/
=h
the more familiar equation is E = m c2
2
2
c c
c
In summary,
1) energy of photon depends only on frequency (or wavelength)
2) intensity of light beam is a measure of # of photons, not energy
3) Light energy can behave both as a wave and as small particles
4) atoms emit light quanta (photons) only of a few specific energies;
this gives rise to the line spectrum (discussed in the previous lecture)
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Wavelike Properties of Matter
de Broglie postulated that matter can behave in some respects like
light. Both light and matter (at the atomic level) are wavelike as well
as particlelike.
This wave/ particle description of light and matter is a mathematical
model that accounts for atomic properties and behavior (math of
quantum mechanics)
Quantum Mechanics and the Heisenberg Uncertainty Principle
A.
Bohr- described the structure of the hydrogen atoms as
containing an electron circling the nucleus where specific
orbitals of the electron correspond to specific energy levels.
B.
Schrodinger- developed the quantum mechanical model of
the atom
- abandoned the idea of an electron as a small particle moving
around the nucleus in a defined path.
- a new theory that concentrates on the electron s wavelike
properties.
C. Heisenberg Uncertainty Principle- both the position and the velocity
of an electron cannot be known beyond a certain level of precision
For example, since the diameter of a hydrogen atom is only 240 pm
(based on it velocity of the single electron and its mass) the uncertainty
in the electron s position is similar in size to the atom itself
Wave Functions and Quantum Numbers
A. Quantum mechanical model of the atomic structure gives a wave
function or orbital - solution to the wave equation.
1) has a specific energy
2) contains information about the an electron s position
(or probability) in 3D space.
3) gives the probability of finding an electron within a given region
4) defines a volume of space around the nucleus where there is a
high probability
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B.
This wave function contains a set of three variables or
quantum numbers. 1) they describe the energy of the orbital
2) defines the the shape and orientation where the electron
probably is
The three quantum numbers are:
1. Principal quantum number (n)
- describes the size and energy level of the orbital.
- a positive integer (n = 1,2,3 )
- there is a increase in the # of allowed orbitals , increase in
orbital size, and increase in energy
Shell = grouping of orbitals according the principal quantum #
2. Angular- Momentum Quantum Number (l )
- defines the shape of the orbital.
- integral value from 0 to n -1. With each shell, there are n
different shapes of orbitals
subshell - grouping of orbitals according the the l number
and are referred to a letters s, p, d, f .
3. Magnetic quantum Number (ml)
- defines the spatial orientation of the orbital
integral value of -l to +l
Within each subshell (same n and same l) there are
(2 l +1) different orientations
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