Atom and Quantum Numbers
Quantum mechanics
Max
Planck and the Black-body radiation:
Max Planck
Planck
studied at the Universities of Munich and Berlin, where his teachers included
Kirchhoff and Helmholtz, and received his doctorate of philosophy at Munich in
1879.
Planck’s
earliest work was on the subject of thermodynamics, an interest he acquired
from his studies under Kirchhoff, whom he greatly admired, He published his papers
on entropy, thermoelectricity, and on the theory of dilute solutions.
The
problems of radiation processes engaged his attention and he showed that these
were to be considered as electromagnetic in nature. Experimental observations
on the wavelength distribution of the energy emitted by a black body as a
function of temperature were at variance with the predictions of classical
physics.
Planck
was able to deduce the relationship between energy and the frequency of
radiation. In a paper published in 1900, he announced his derivation of the
relationship: this was based on the revolutionary idea that the energy emitted
by a resonator could only take on discrete values or quanta. The energy for a
resonator of frequency v is hv where h is a universal
constant, now called Planck’s constant.
Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit: E =hv Where h is Planck's constant, (the value of which is 6.63×10−34 Js), and ν is the frequency of the radiation. Physicists now call these quanta as photons, and a photon of frequency ν will have its own specific and unique energy. The total energy at that frequency is then equal to hν multiplied by the number of photons at that frequency.
Planck and Nernst, seeking to clarify the increasing number of contradictions, organized the First Solvay Conference (Brussels 1911). In recognition of Planck's fundamental contribution to a new branch of physics, he was awarded the Nobel Prize in Physics in 1918 (he actually received the award in 1919).
Photo-emission from atoms, molecules, and solids
Albert Einstein
In 1896 Albert Einstein entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma, he acquired Swiss citizenship and, as he was unable to find a teaching post, he accepted a position as a technical assistant in the Swiss Patent Office. In 1905 he obtained his doctor’s degree.
Light, Einstein said, is a beam of
particles whose energies are related to their frequencies according to Planck's
formula. When light beam is directed at a metal, the photons collide with the
atoms. If a photon's frequency is sufficient to knock off an electron,
the collision produces the photoelectric effect.
Electrons that are bound in atoms, molecules, and solids each occupy distinct states of well-defined binding energies. When light quanta deliver more than this amount of energy to an individual electron, the electron may be emitted into free space with excess (kinetic) energy that is hv higher than the electron's binding energy. The distribution of kinetic energies thus reflects the distribution of the binding energies of the electrons in the atomic, molecular or crystalline system: an electron emitted from the state at binding energy EB is found at kinetic energy Ek = hv - EB This distribution is one of the main characteristics of the quantum system and can be used for further studies in quantum chemistry and quantum physics.
The phenomenon of emission of electrons from the surface of the metal when the light of suitable frequency falls on it is called the photoelectric effect. The current produced due to emitted electrons is called photo-current. The photoelectric effect proves the quantum nature of radiation.
Compton scattering :
The Compton effect is a process in which x-rays collide with electrons and are scattered.
By the early 20th century, research into the interaction of X-rays with the matter was well underway. It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle θ and emerge at a different wavelength related to θ. The experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.
In 1923, Compton published a paper in the Physical Review that explained the X-ray shift by attributing particle-like momentum to
light quanta (Einstein had proposed light quanta in 1905 in explaining the
photo-electric effect, but Compton did not build on Einstein's work). The
energy of light quanta depends only on the frequency of the light. In his
paper, Compton derived the mathematical relationship between the shift in
wavelength and the scattering angle of the X-rays by assuming that each
scattered X-ray photon interacted with only one electron. His paper concludes
by reporting on experiments that verified his derived relation: 
The de Broglie hypothesis:
Louis Victor de Broglie was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. de Broglie suggested that particles can exhibit the properties of waves. In his 1924 Ph.D. thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.
In 1923, Louis de Broglie proposed a hypothesis to explain the theory of the atomic structure. By using a series of substitutions de Broglie hypothesizes particles to hold the properties of waves. Within a few years, de Broglie's hypothesis was tested by scientists shooting electrons and rays of light through slits. What scientists discovered was the electron stream acted the same way as light, proving de Broglie correct. He gave the relation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of a particle, moving at a velocity v. The above equation is called de Broglie equation and 'λ' is called the de Broglie wavelength. Thus the significance of the de Broglie equation lies in the fact that it relates the particle character with the wave character of matter.
de Broglie equation states that a matter can act as waves much like light and radiation, which also behave as waves and particles. The equation further explains that a beam of electrons can also be diffracted just like a beam of light. In essence, the de Broglie equation helps us understand the idea of moving particles of matter having a wavelength.
De Broglie won the Nobel Prize for Physics in 1929, after the wave-like behaviour of matter was first experimentally demonstrated in 1927.
The DPG held a celebration, during which the Max-Planck medal (founded as the highest medal by the DPG in 1928) was awarded to French physicist Louis de Broglie.
Erwin
Schrodinger
Erwin Schrödinger proposed the quantum mechanical model of the atom, which treats electrons as matter waves. ... The square of the wave function, ψ2 , represents the probability of finding an electron in a given region within the atom.
Following up on de Broglie's ideas, physicist Peter Debye made an offhand comment that if particles behaved as waves, they should satisfy some sort of wave equation. Inspired by Debye's remark, Schrödinger decided to find a proper 3-dimensional wave equation for the electron. He was guided by William R. Hamilton's analogy between mechanics and optics, encoded in the observation that the zero-wavelength limit of optics resembles a mechanical system—the trajectories of light rays become sharp tracks that obey Fermat's principle, an analog of the principle of least action. The equation he found is:
Erwin Rudolf Josef Alexander Schrödinger was a Nobel Prize-winning Austrian-Irish physicist who developed a number of fundamental results in quantum theory: the Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time.
The Schrodinger equation
is one of the most fundamental equations of quantum physics. The Schrodinger
equation is basically a differential equation and is widely used in Chemistry and
Physics to solve problems based on the atomic structure of matter.
Schrodinger wave
equation describes the behavior of a particle in a field of force or the change
of a physical quantity over time. Erwin Schrödinger who developed the equation
was awarded the Nobel Prize in 1933.
EΨ(r) = [−ℏ2/2m ∇2 +V(r)]Ψ(r)
Time-independent Schrödinger equation (single nonrelativistic particle)
Hydrogen atom:
The Schrödinger equation for the hydrogen atom (or a hydrogen-like atom) is
where : q is the electron charge, r is the position of the electron relative to the nucleus,
r = | r | is the magnitude of the
relative position, the potential term is due to the Coulomb interaction,
wherein ε0 is the permittivity of free space and 
is the 2-body reduced mass of the hydrogen nucleus (just a proton) of mass
mp and the electron of mass mq
.
The wavefunction for hydrogen is a function of the electron's coordinates, and in fact, can be separated into functions of each coordinate. Usually, this is done in spherical polar coordinates:
The solution to this equation leads to the quantum numbers[as in the table
below]
Key points
Louis de Broglie proposed that all particles could be treated as matter waves with a wavelength λ, given by the following equation: λ= h / mv
·
Erwin Schrödinger proposed the quantum
mechanical model of the atom, which treats electrons as matter waves.
·
Schrödinger's equation, H^ψ =Eψ, can be solved to yield a series of wave
function ψ, each
of which is associated with an electron binding energy, E.
·
The square of the wave function, ψ, squared, represents the probability
of finding an electron in a given region within the atom.
·
An atomic orbital is defined as the region
within an atom that encloses where the electron is likely to be 90% of the
time.
·
The Heisenberg uncertainty principle states
that we can't know both the energy and position of an electron. Therefore, as
we learn more about the electron's position, we know less about its energy, and
vice versa.
·
Electrons have an intrinsic property called
spin, and an electron can have one of two possible spin values: spin-up or
spin-down.
·
Any two electrons occupying the same orbital
must have opposite spins.
Quantum mechanics started after Plank's concept of Photon.
ReplyDelete