QUANTUM AND NUCLEAR PHYSICS

Wave Particle DualityIn some situations light exhibits properties that are

wave-like or particle like.Light does not show both properties at the same

time and place.Wave packet or photon is particle like in its finite

size but wave like in its varying amplitude.

The amplitude is a measure of the probability of finding a photon at a particular place.

A large amplitude is a high probability of finding the photon

A ComparisonWave – Like• Diffraction – bending

around obstacles

• Interference

• Polarisation

• Reflection

• Refraction

Particle• Line emission spectra

• Exerts radiation pressure or force

• Photoelectric effect

• Gravitational bending of light eg around the Sun

Planck’s Quantum Theory

Classical Physics

• Describes electromagnetic energy as a wave.

Quantum Mechanics

• Describes electromagnetic energy as a

“particle” equivalent.

Planck’s Quantum Theory

• 1901 Planck proposed that electromagnetic energy was quantised and only occurred in discrete amounts.

(not continuous) called quanta

• A photon is a monochromatic (single frequency) quantum of EM energy.

• Planck’s Law states that the energy of each photon is directly proportional to its frequency.

• energy α frequency

• Constant of proportionality is h Planck’s constant

6.626 x 10-34 J.s

• photon = Planck’s x photon

energy constant frequency

E = h . f (J)

Energy of a photon

Since the speed of electromagnetic radiation

is given by:

where c = 3.00 x 10 8 ms-1

then

This is the energy of a photon of a wavelength of electromagnetic radiation

.fc

hc

E

1.What is the energy of a quantum of green light of frequency 5.0 x 1014 Hz?

2. How much energy is contained in a photon of UV of wavelength 1.0 x 10-7 m

3. Calculate the frequency and wavelength of a photon of light with energy 4.0 x 10 -19 J

Classical Predictions

• Intensity– as light increases number of photo electrons increases

• Emission time – low intensity light longer emission time

• Frequency – emission is independent of frequency

• Energy – as light intensity increases the kinetic energies of the photo- electrons increases

Experimental Results

• Intensity – number of photoelectrons increased with intensity

• Emission – instantaneous

• Frequency – emission is frequency dependent. Below cut-off frequency no electrons emitted

• Energy- as intensity incr KE max stayed constant. KE is frequency dependent with type of material

Photoelectric Effect

• metals bombarded with high frequency light emit electrons (photoelectrons)

• occurs in solid, liquids and gases

• first discovered by Hertz in 1887

Einstein’s Theory• Based his explanation of the photoelectric

effect on Planck’s quantum idea.

He proposed that:• energy was in a particle called a photon• Each photon had an energy of E = hf• A photon could give up all its energy to one

electron but not part “all or nothing”• The maximum KE of the emitted electron

was equal to the initial photon minus the work done in overcoming the attractive forces near the metal surface.

• Ф is the work function, the minimum energy needed to escape the nuclear attractive force on the electrons.

• Ф is given in electron volts

• Ф = h.f0 where f0 is the cut-off or threshold frequency

• KEMAX = h.f - Ф

½ mv2 = h.f – Ф

Electron volt

• This is the energy gained by an electron as it moves through an electric field of 1V

from

• EP = qV or eV

charge on an electron is 1.6 x 10 -19 C

1eV = 1.6 x 10 -19 C x 1V

= 1.6 x 10 -19 J

The threshold frequency of rubidium is 5.0 x 1014 Hz. Find

• a)the work function and

• b) the max velocity of electrons ejected by light of a frequency of 8.0 x 10 14 Hz

( the mass of an e is 9.1 x 10-31 kg

Do now

• Write down Einstein’s photoelectric equation and explain the meaning of each symbol

• What is meant by threshold frequency

calculate the f0 of a material having a work function of 4.5eV

1.09 x 1015 Hz

• The f0 for a metal is 3 x 1014 Hz. If blue radiation of frequency 7 x 1014 Hz falls on the material, find

(a) Energy of incident photon

(b) work function

(c) max KE of ejected photoelectrons

(d) max velocity of ejected photoelectrons. (mass of electron = 9 x 10-31 kg

answers(a) 4.64 x 10 -19 J

(b) 1.99 x 10-19 J

(c) 2.65 x 10-19 J

(d) 7.67 x 105 ms-1

Photocell and Planck’s constant

Summary

Photoelectric Effect• Define work function• Energy is α frequency

E α f or = hf• Define threshold f• Photoelectron emission is

instantaneous• Increase Intensity = more

e emitted• Insufficient energy or Φ

metal heats up but no photoemission

Wave/ Particle Duality• Particle like nature eg.

line emission spectra, radiation pressure or force

• Wave like nature eg. Interference light passing through slits;

and diffraction – laser light falling on a screen to produce a central bright spot

Atomic Spectra• Newton identified components of white light.• Bunsen & Kirchoff identified elements by the spectra

produced.Gases can be excited by heating or by electrical dischargeThere are three types of spectra:1. Continuous spectrum – all frequencies represented;

usually a heated light source eg Sun

2. Emission spectrum- when an excited atom returns to its ground state, it emits e.r. of particular frequencies only. The energy the electron loses jumping from a higher to a lower orbit is emitted as a photon. E=hf

3. Absorption spectrum – a photon of energy can raise an electron to a higher orbit. If white light is passed through a gas containing sodium, certain frequencies will be removed

Absorption and Emission

Atomic Line Spectra When excited by heat or an electrical discharge the

atoms gives off particular frequencies of light.

The Balmer formula can be used to predict the

wavelengths of visible light. This was later modified by Rydberg to give:

where S = Series number

L= Line number (S+1)

R= Rydberg constant = 1.1 x 107 m-1

22

111

LSR

Hydrogen Spectra AnalysisRydberg’s formula also applies to the series of lines in the

infra-red and ultraviolet spectrum

1. Lyman formula (ultra-violet range)

2. Balmer formula (visible light range)

3. Paschen formula (infra-red

22

1

1

11

nR

22

1

2

11

nR

22

1

3

11

nR

The lines of the hydrogen spectrum correspond to particular frequencies and energy levels given by E=hf

These levels are not evenly spaced but vary by 1/n2 according to Rydberg.

When the electron is in the lowest level or ground state, then n=1. The highest level is called the ionisation level, n=α

Hydrogen Atom

Bohr’s Hydrogen Atom (1913)

1. electrons have fixed amounts of energy (quanitsed); they revolve around the nucleus in allowed orbits or stationary states without radiating energy

2. Electrons can jump from one energy level to another by either absorbing or emitting a photon of light equal to the difference in energy levels

ΔE=|E - E| = hf

3. Angular momentum (mvr) is quantised and can only take multiples : L = n

where n is the principal quantum number2h

Calculating Energy Emissions/Absorptions

What are the possible

energies that an

emitted photon could

have?

Ephoton=hf=En- Em = hc/λ

n=3

n=2

n=1

-1.5eV

-3.4eV

-13.6eV

For n=3 to n=2

E= E3 – E2

= -1.5 – (-3.4)

=1.9eV

For n=3 to n=1

E = E3 – E1

= -1.5 – (-13.6)

= 12.1eV

For n=2 to n=1

E = E2 – E1

= -3.4 – (-13.6)

= 10.2eV

values +ve for emission

(b) E = hf = hc/λ so

λ=hc/E

E values are in eV; convert to Joules

1eV = 1.6 x 10 -19 J

h = 6.62 x 10-34Js

c = 3.0 x 108ms-1

• From Rydberg’s formula

• The energy of the photon emitted is

This is the energy difference between 2 electron energy levels.

Electrons can only exist with energy levels of

Where n=1,2,3….. Where n is the quantum number

Limitations of Bohr’s Model

Does not explain

• why electrons have fixed energy levels

• Why some spectral lines are more intense than others

• the presence of hyperfine spectral lines

• Spectra for atoms larger than the hydrogen atom – one electron