Atomic Physics – review

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Atomic Emission Spectra
All object emit thermal radiation characterized by a continuous distribution of wavelengths
A discrete line of spectrum is observed when a low pressure gas is subjected to an electrical discharge
Emission spectroscopy
observation of spectral lines
atomic hydrogen
simplest line spectrum
Unique spectra
a technique for identifying the elements present in unknown samples
Absorption spectrum
is obtained by passing white light from continuous source through a gas or a dilute solution of the element being analyzed
This consists of a series of dark lines superimposed on the continuous spectrum of the light source
Thomson’s model of atom
A volume of positive charge
Electrons embedded throughout the volume
The atom as a whole would be electrically neutral
Rutherford’s tin foil experiment
A beam of positively charged alpha particles hit and are scattered from a tin foil target
Large deflections could not be explained by Thomas model
Early models of the atom: Rutherford
Planetary model
Based off the results of tin foil experiment
Positive charged is concentrated in the center of the atom, called the nucleus
Electrons orbit the nucleus like planets the sun
Difficulties with Rutherford idea
Atoms emit certain discrete characteristic frequencies of electromagnetic radiation
-this model is unable to explain this
-this electron was undergoing centripetal acceleration
-it should radiate electromagnetic waves of the same frequency
-the radius should steadily decrease as the radiation is given off
– the electron should eventually spiral into the nucleus – it doesnt
Bohr theory of Hydrogen
His model includes both classical and non classical ideas
he applied planck’s idea of quantized energy levels to rutherford’s orbiting electrons
This model is now called obsolete
It has been replaced by probabilistic quantum mechanical theory
The model can still be used to develop ideas of energy quantization and angular momentum quantization as applied to atomic sized systems
Bohr’s postulates for hydrogen 1
The electron moves in circular orbits around the proton under the electric force of attraction
The Coulomb force produces the centripetal acceleration
Bohr’s postulates for hydrogen 2
Only certain electron orbits are stable – stationary states – orbits in which the atom does not emit energy in the form of electromagnetic radiation
So the energy of the atom remains constant
Bohr’s postulates for hydrogen 3
Radiation is emitted by the atom when the electron makes a transition from a more energetically initial stationary state to a lower energy stationary state
Ei – Ef = hf
Bohr’s postulate for hydrogen 4
The size of the allowed electron orbits is determined by a condition imposed on the electron’s orbital angular momentum
The allowed orbits are those for which the electron’s orbital angular momentum about the nucleus is quantized and equal to an integral multiple of h
Bohr’s postulates
1 – from classical mechanics – treats the electron in orbit around the nucleus in the same way we treat a planet in orbit around a star
2. new idea – it was completely at odd with the understanding of electromagnetism
3. principle of conservation of energy
4. new idea – had no basis in classical physics
Bohr’s Correspondence principle
quantum physics agrees with classical physics when the differences between quantized levels become infinitely small. Similar to Newtonian mechanics being a special case of relativistic mechanics when v<<
Quantum model of the hydrogen atom
The difficulties with the Bohr model are removed when a full quantum model involving Schrodinger equation is used to describe the hydrogen atom
The potential energy function for hydrogen
Quantum numbers
When a full set of boundary conditions are applied, we are led to three different numbers, for each allowed state
These are restricted to integer values
They correspond to three degrees of freedom
Principle quantum number, n
The potential energy function depends only on the radial coordinate r
The energies of the allowed states in the hydrogen atom are the same En values found from Bohr theory
The value of n are integers that can range from 1 to infinity
Orbital quantum number, I
It is associated with orbital angular momentum of the electron
The values of I , are integers that can range from 0 to n-1
Magnetic quantum number, mI
It is also associated with the angular orbital momentum of electron and is an integer
The values of m, are integers that can range from -I to I
Shells
Historically all states having the same principle quantum number are said to be from the same shell
Shells are identified by letter K, L, M for which n = 1,2,3
All states having the same values of n and I are said to form a subshell
the letters s, p, d, f ,g and ha are used to designate the subshells from which I = 0, 1,2 ,3,…
Atomic shell notation
N
1 k
2 L
3 M
4 N
5 O
6 P
Atomic subshell notations
L
0 s
1 p
2 d
3 f
4 g
5 h
Electron clouds
Wave function – the probability to finding the electron as a function of distance from the nucleus for the hydrogen atom in 1s ground state
The atom has no sharply defined boundaries as suggested by the Bohr theory
The charge of the electron is extended throughout a diffuse region of space called the electron cloud
The orbital quantum number I
The magnitude of the angular momentum of an electron moving in a circle of radius r is L=Mevr
The magnetic quantum number mi
the atom possesses an orbital angular momentum
there is a sense of rotation of the electron around the nucleus so that a magnetic moment is present due to this angular momentum
there are distinct directions allowed for the magnetic moment vector with respect to the magnetic field vector
The spin of quantum number ms
electron spin does not come from the Schrodinger equation.
Additonal quantum states can be explained by requiting a fourth quantum number for each state
only two directions exist for electron spins
the electron can have spin up and spin down this can have +1/2 or -1/2 spin
Pauli Exclusion principle
no two electrons can ever be in the same quantum state, no two electrons in the same atom can have the same set of quantum numbers
Hands rule
when an atom has orbitals of equal energy the order in which they are filed by electrons is such that a maximum number of electrons have unpaired spins
Xray spectra
Xrays are the result of the slowing down of high energy electrons as the strike a metal target
The descrete lines are called characteristic x rays
These are created when:
A bombarding electron collides with a target atom
The electron removes an inner shell electron from orbit
Stimulated absorption
when a photon has energy hf equal to the difference in energy levels it can be absorbed by the atom, this is because the photon stimulates the atom to make the upward transition
The absorption of the photon causes some of the atoms to be raised to excited states
Spontaneous emission
once an atom is in an excited state the excited atom can make a transition to a lower energy level
Stimulated emission
may occur when the excited state is a metastable state, this is when it lasts in excited state for a long time and therefore there are two photons with identical energy the emitted photon and incident photon
Lasers
Light Amplification by Stimulated Emission of Radiation
Laser light is coherent – individual rays in a laser beam maintain a fixed phase relationship with each other
Laser light is monochromatic – the light has a very narrow range of wavelengths
Laser light has a small angle divergence – the beam spreads out very little ever over long distances
it is equally probable that an incident photon would cause atomic transition upward or downward
The excited state in a laser must be in the metastable state
Categories: Atomic Physics