QUANTUM MECHANICS

1. QUANTUM THEORY
Frederick Nti
Energy Quantization

2. • It was once thought that the motion of atoms and subatomic particles could
be expressed using classical mechanics
• The laws of motion introduced by Isaac Newton
• these laws were very successful at explaining the motion of everyday objects
and planets.
• However, experimental evidence showed that classical mechanics failed
when it was applied to particles as small as electrons
• It took until the 1920s to discover the appropriate concepts and equations
for describing them.
• The concepts of this new mechanics are described in quantum mechanics
The Origins of Quantum Mechanics

3. Energy quantization
• The quantization of energy refers to the absorption or emission of energy in
discreet packets, or quanta.
• As the intensity of electromagnetic energy increases or decreases, it steps up or
down from one quantized level to another, rather than follow a smooth and
continuous curve.
• The establishment of energy quantization called for the replacement of classical
mechanics
• Energy quantization became evident under three main studies
 The black-body radiation
 Heat capacities
 Atomic and molecular spectra

4. Energy quantization
• Black body is a material capable of emitting and absorbing all
wavelengths of radiations uniformly.
• The classical approach to the description of black-body radiation
results in the ultraviolet catastrophe.
• The prediction of classical physics that an ideal black body at thermal
equilibrium will emit radiation in all frequency ranges, emitting more
energy as the frequency increases.
• The sum of emissions in all frequency ranges suggest that a blackbody
would release an infinite amount of energy, contradicting the
principles of conservation of energy
• This drew attention to the need of a new model for the behavior of
blackbodies
Black Body Radiation

5. Energy quantization
Black Body Radiation
• A good approximation to a blackbody is a pinhole in an empty
container maintained at a constant temperature
• Any radiation leaking out of the hole has been absorbed and re-
emitted inside so many times as it reflected around inside the
container that it has come to thermal equilibrium with the walls
• The 19th century approach adopted to explain black-body radiation
was to calculate the energy density, dE
Rayleigh–Jeans law for the density of states

6. Energy quantization
Black Body Radiation
• Rayleigh–Jeans law is quite successful at long wavelengths (low frequencies)
• But fails badly at short wavelengths (high frequencies).
• The equation therefore predicts that oscillators of very short wavelength
(corresponding to ultraviolet radiation, X-rays, and even gamma rays) are
strongly excited even at room temperature.
• This absurd result, implies that a large amount of energy is radiated in the high-
frequency region of the electromagnetic spectrum
• This is called the ultraviolet catastrophe.
According to classical physics, even cool objects should
radiate in the visible and ultraviolet regions, so objects
should glow in the dark; there should in fact be no
darkness

7. Energy quantization
• To avoid this catastrophe, Max Planck proposed that the electromagnetic field
could take up energy only in discrete amounts
• This is called quantization of energy
• His theory is expressed in the relation below:
• This fits the experimental curve at all wavelengths
• For long wavelengths, and the denominator in the Plank distribution
can be replaced by
Black Body Radiation

8. Energy quantization
• The French scientists Pierre-Louis Dulong and Alexis-Thérèse Petit determined the
heat capacities, CV = (∂U/∂T)V of a number of monatomic solids.
• They proposed that the molar heat capacities of all monatomic solids are the same
and close to 25 J K−1 mol−1.
• Dulong and Petit’s law is easy to justify in terms of classical physics in much the
same way as Rayleigh attempted to explain black-body radiation.
• Unfortunately, significant deviations from their law were observed when advances
in refrigeration techniques made it possible to measure heat capacities at low
temperatures.
Heat Capacities

9. Energy quantization
• It was found that the molar heat capacities of all monatomic solids are lower than
3R at low temperatures, and that the values approach zero as T→0.
• To account for these observations, Einstein assumed that each atom oscillated
about its equilibrium position with a single frequency ν.
• He then invoked Planck’s hypothesis to assert that the energy of oscillation is
confined to discrete values, and specifically to nhν, where n is an integer.
• Einstein discarded the equipartition result, calculated the vibrational contribution
of the atoms to the total molar internal energy of the solid and obtained the
expression known as the Einstein formula:
Heat Capacities

10. Energy quantization
• The most compelling and direct evidence for the quantization of energy comes
from spectroscopy
• Spectroscopy is the detection and analysis of the electromagnetic radiation
absorbed, emitted, or scattered by a substance.
• The obvious feature of both is that radiation is emitted or absorbed at a series of
discrete frequencies.
• If the energy of an atom decreases by ΔE, the energy is carried away as radiation
of frequency ν, and an emission ‘line’, a sharply defined peak, appears in the
spectrum.
• We say that a molecule undergoes a spectroscopic transition, a change of state,
when the Bohr frequency condition
ΔE = hν
Atomic & Molecular Spectra

11. THANK YOU !