# Atomic Physics – review

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

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

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

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

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

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

-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

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

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

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

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

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

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

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

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

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

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

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,…

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

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

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 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

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

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

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

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

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