Quantum theory replaced classical mechanics in describing the motion of small particles like electrons. It introduced the concept of energy quantization, where energy can only be absorbed or emitted in discrete packets called quanta. This helped explain phenomena like blackbody radiation, heat capacities of solids, and atomic/molecular spectra that classical mechanics could not. Max Planck proposed quantizing energy to avoid the "ultraviolet catastrophe" where classical physics predicted infinite radiation from hot objects. Einstein further applied the idea to explain heat capacities at low temperatures. Spectroscopy also showed radiation absorbed/emitted at discrete frequencies, supporting energy quantization.

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

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