Download Quantum Theory of the Atom The Wave Nature of

Quantum Theory of the Atom
The Wave Nature of Light
Electromagnetic radiation carries energy = radiant energy
some forms are visible light, x rays, and radio waves
Wavelength ( λ) is the distance between any 2 adjacent identical points of a wave
Frequency ( ν) is the number of wavelengths of that wave that pass a fixed point
in one unit of time
c= νλ
where the speed of light = c = 3.00 x 108 m/s
Example:
What is the wavelength of the yellow light given off by a sodium vapor lamp used for public
lighting has a wavelength of 589 nm. What is the frequency of this radiation?
What is the wavelength of the yellow sodium emission, which has a frequency of 5/09 x 1014s-1?
Electromagnetic spectrum - the range of wavelengths of electromagnetic radiation.
Max Plank (1900) described the intensity of light of various frequencies.
He determined that an atom could have only certain energies of vibration, E,
E=nhν
n = 1, 2, 3, ….
where h = Plank's constant = 6.63 x 10-34 J.s
n = quantum numbers
Planck believed that energy can be released or absorbed by atoms only in "chunks"
of some minimum size called quantum (fixed amount). These chunks are emitted
or absorbed in whole number multiples of hν, 2hν, 3hν …
Albert Einstein (1905) used Planck's theory to explain photoelectric effect. He
postulated that light consists of 'quanta" or particles of electromagnetic energy,
with E proportional to the observed frequency of the light - now known as a
photon.
E = hν
Photoelectric effect is the ejection of electrons from the surface of a metal or from
another material when light shines on it.
Calculating the Energy of a Photon
The red spectral line of lithium occurs at 671 nm. Calculate the energy of one
photon of this light.
Niels Bohr (1920s) applied a new theory to the simplest atom, hydrogen, using
Planck's and Einstein's theories and J.J. Balmer's equation. The visible spectrum of
hydrogen could be reproduced by a simple formula:
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= (1.097 x 107/m) ( 2-
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Bohr's postulates to account for the stability of the hydrogen atom and the line
spectrum of the atom were:
1. Energy level Postulate - an electron can have only specific energy values in an
atom which are called energy levels.
E = -
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where RH is an energy constant = 2.179 x 10 -18J and n is an integer and is called
the principle quantum number
2. Transitions between energy levels - an electron can change energy levels by
going from one energy level to the another energy level.
∆E = Ef - Ei
hν = -∆E = - (Ef - Ei)
If ∆E is + when nf > ni which means radiant energy is absorbed
If ∆E is - when nf < ni which means radiant energy is emitted
Calculate the wavelength that corresponds to the transition of the electron from n=4 to n=2 state
of the hydrogen atom. Is the light absorbed or emitted by the atom?
Quantum Mechanics, or wave mechanics, is a branch of physics that
mathematically describes the wave properties of submicroscopic particles.
de Broglie (1923) considered that if radiant energy behaved like a stream of
particles, could matter?
Electrons in an orbit could be thought of as a wavelength. Given these particles had
a mass, m, and a speed of ʋ.
λ = h / mʋ
Calculate the wavelength of an electron with velocity of 5.9 x 106 m/s . the mass of
electron is 9.11 x 10-28 g
Heisenberg (1927) showed from quantum mechanics that it is impossible to know
simultaneously both the position and the momentum of a particle such as an
electron.
Uncertainty Principle is a relationship that states that the product of the uncertainty
in position and the uncertainty in the momentum of a particle can be no smaller
than Planck's constant divided by 4π.
(∆x) (∆px) ≥ h / 4 π
According to quantum mechanics, each electron in an atom is described by four
different quantum numbers, three of which (n, l and ml) specify the wave function
that gives the probability of finding the electron at various points in space.
A wave function for an electron in an atom is called an atomic orbital.
Each orbital describes a specific distribution of electron density in space.
1. Principal quantum Number (n)
this is the one on which the energy of an electron in an atom principally
depends; it can have any positive value
2. Angular Momentum Quantum Number (l)
this one distinguishes orbitals of a given n having different shapes; it can
have any integer value from 0 to n-1
3. Magnetic Quantum Number (ml)
this one distinguishes orbitals of given n and l - that I, of given energy and
shape but having a different orientation in space; the allowed values re the integers
-l to +l
4. Spin Quantum Number (ms)
this one refers to the two possible orientations on the spin axis of an
electron; possible values are +1/2 and -1/2