Download Atoms and quantum phenomena

Atoms and quantum phenomena
SASP 10th June 2010
Decay
• 4 natural radioactive decay series
• (starting with Thorium, Neptunium, Uranium, Actinium)
• spontaneous nuclear reactions: mother, daughter, radiation emitted
• (with time) all 4 series end at Pb (lead) [Pb is nice and stable]
Relative amounts of isotopes can give information about
age of objects
Stability and the N-Z Graph
• Darker isotopes shown here
are stable. Radioisotopes
are unstable.
• As the proton number
increases, an increasing ratio
of neutrons is needed to form
a stable nucleus
A spot of history
• Fission
1932: neutron discovered by Chadwick
1934 onwards: experiments done by Fermi et al in Rome - neutron irradiation of
elements, starting with lightest & working through the periodic table up to Uranium.
Expected transuranic elements. Hahn, Strassman, Lise Meitner repeat with U.
235
92
235
92
U  n  K  Ba 3 n  energy
1
92
141
1
0
36
56
0
U  n  Sr  Xe  2 n  energy
1
94
140
1
0
38
54
0
with a critical mass of U, neutrons emitted give a ‘chain reaction’
• Fusion
small nuclei combine, releasing more energy than fission e.g.
2
1
H11H23 He  energy
Energy, mass and decay
Let’s look at some numbers and see if they
make sense.
Mass of a proton = 1.673 x 10-27kg
Mass of a neutron = 1.675 x 10-27kg
Mass of a alpha particle (ppnn)
= 6.643 x 10-27kg
Energy, mass and decay
Before we go on, kg is not the most helpful unit here
so we are going to use u, the atomic mass unit
wherever possible. 1u = 1/12 the mass of a neutral
12C atom (i.e. including its six electrons)
1u = 1.66056 x 10-27kg
Mass of a proton = 1.007276u
Mass of a neutron =1.008665u
Mass of an electron = 0.000549u
Mass of Hydrogen atom = 1.007825u
Mass of Helium Atom = 4.002603
Mass of a alpha particle = 4.001505u
Measurement interlude
• Whilst we are at it, small amounts of energy
mean that the Joule is a bit cumbersome. So
we use the Electron Volt
• Definition: The amount of kinetic energy
gained by a single unbound electron when it
accelerates through an electric potential
difference of one volt. (Not SI, experimental)
• 1eV = 1.602 x 10-19J
Hmm, the sums don't add up
‘Missing mass’ and binding energy
• The difference may not seem that much, but if
you consider a helium atom (ppnnee) then we
see that the atom is 0.03077u ‘too light’.
Which is about 55 electrons.
• In general all atoms are lighter than their
constituent parts. In particular it is in the
nucleus that this mass defect is particularly
apparent. Somehow protons and neutrons are
lighter inside the nucleus than outside.
‘Missing mass’ and binding energy
• Protons and neutrons ejected from the nucleus
regain their missing mass when they are outside
the nucleus. The explanation for this comes with
the idea of ‘binding energy’.
• The mass defect (ΔM) of the nucleus is the
difference between the total mass of all it's
separate nucleons and the mass of the nucleus
itself.
• The binding energy of a nucleus (ΔE) is the
energy released when the nucleus is assembled
from its constituent nucleons. It is equal to the
energy needed to separate the nucleus into
individual nucleons.
‘Missing mass’ and binding energy
• In the beginning, when the nuclei were
created from the cosmic soup of fundamental
particles, the strong nuclear force (that holds
p and n together) had to do work to bring
them together. The energy to do this work
came from a direct conversion of mass to
energy, which is why the assembled nucleus is
lighter than the individual nucleons. [We tend
to ignore electrons and comparatively they
make a negligible contribution]
‘Missing mass’ and binding energy
• In the nucleus, the nucleons are in a lower
energy state. In order to separate the nucleus
into it’s nucleons, an amount of work is
needed to be done them. This amount of
energy needed to pull them apart is equal to
the work done to bring them together (by the
strong force) in the first place. This energy is
converted into matter, resorting the nucleons
to their original masses.
The Strong Force
• The strong force (strong interaction) is
observable in two areas:
• Large scale – it binds protons and neutrons
together to form the nucleus of an atom.
• Smaller scale – it holds quarks and gluons
together to form the proton, the neutron and
other particles.
So how do the mass and energy relate
to each other?
Binding energy
• Clearly, there will be more ‘lost’ mass and more
‘gained’ energy per nucleon so the total binding
energy in a nucleus is not a helpful number to give
in order to give us a sense of how ‘stuck together’
a nucleus is.
• This idea of how ‘stuck together’ it is, is important
as it essentially tells us how stable the nucleus is
and this stability idea (as mentioned earlier) is
much more useful. Stability depend upon energy.
• Binding energy per nucleon is more useful,
average amount of glue per piece stuck together
Binding energy per nucleon
Same graph, other way up
An even closer look (Some LOs)
• explain atomic line spectra in terms of
electron energy levels and a photon model of
electromagnetic radiation
• describe and explain the photoelectric effect,
• solve quantitative problems using photon
energy
• be aware of the of the wave nature of
electrons and calculate their wavelength
Teaching challenges
• Whereas classical physics rewards students
who can picture what is happening, quantum
theory defies visualisation.
• Abstract and counter-intuitive ideas need to
be linked to visible phenomena and devices,
including some already familiar to students.
• Most A-level specifications trivialise the
teaching of quantum phenomena and fail to
distinguish it properly from classical physics.
Scientific explanation
• correlates separate observations
• suggests new relations and directions
• gives testable hypotheses (empirical ‘acid
test’)
Unifications in physics
(a bit more history)
Mechanical theory
Electromagnetic theory
(Newton, 1687)
Entities: particles, inertia, force
that lies along a line between
interacting particles.
(Maxwell, 1864)
Entities: electric & magnetic fields,
force that is perpendicular to both
field & motion.



celestial motions
terrestrial motions, in 3-D
heat (kinetic theory)



magnetism
electricity
optics
Relativity theory (Einstein, 1905 & 1916) unites all phenomena above
Quantum theory
(Planck 1900; Einstein 1905,16&17; Bohr & Heisenberg 1925; Schrodinger
1926; Dirac 1927; Bethe, Tomonaga, Schwinger, Feynman & Dyson 1940s …)
 atoms and nuclei
Dissolves the classical distinction between point particles & nonlocal fields/waves. Quantum objects manage both at once.
What went wrong?
Classical physics could not explain
• line spectra
• electron configuration in atoms
• black body radiation
• photoelectric effect
• specific thermal capacity of a crystalline solid
• Compton scattering of X-rays
The end of the mechanical age
1.
Things move in a continuous manner. All motion, both in the large and
small, exhibits continuity.
2.
Things move for reasons. All motion has a history, is determinable and
predictable.
3.
The universe and all its constituents can be understood as complex
machinery, each component moving simply.
4.
A careful observer can observe physical phenomena without disturbing
them.
• Inside atoms, all of these statements
proved false – we need another way of
looking at the world on this scale
‘Quantum theory’
• Quantum mechanics
•
(electrons in atoms i.e. Chemistry, superconductors, lasers, semiconductor
electronics)
• Quantum field theory
• quantum electrodynamics (interactions of light & matter, interactions of
charged particles, annihilation & pair production)
• electroweak unification (weak force + electromagnetism)
• quantum chromodynamics (quarks & gluons)
• Explains everything except gravity.
Quantum theory in essence
• only the probability of events is predictable
• whatever happens in between emission and absorption, light is
always emitted and absorbed in discrete amounts of energy.
Einstein: ‘God does not play dice.’
Bohr: ‘Anyone who is not shocked by quantum theory has not fully
understood it.’
Feynman: ‘things on a small scale behave nothing like things on a large
scale.’ ‘I hope you can accept Nature as She is – absurd.’
Quantum theory in essence
How photons travel
• Photons seem to obey the command ‘explore all paths’. All
the possibilities can be added up in a special way and used
to predict what happens.
Particle physics
• The same approach is used to work out how quantum
particles
• change into one another - neutron (udd) decays to proton
(uud)
• interact with one another - electrons repel by exchanging a
photon
Scientists agree to differ
• Agreed formalism, different interpretations
Does the quantum world really exist, or is
there only abstract quantum physical
description?
•
Responses include:
• Copenhagen interpretation (There is no objective reality. A quantum
system has no properties until they are measured.)
• ‘many worlds’ (All things happen, in a branching universe.)
• non-local, hidden variables (an attempt to restore realism)
Line spectra
There is a ‘ladder’ of energy levels in the atom.
Changes in electron arrangement correspond to the emission
or absorption of a photon.
E  E  hf 
2
1
hc

where h is the Planck constant,
Line spectra
This is what explains the line spectra
that we have covered before. The
colour palette could be imagined as a
visual ‘map’ of the electron
configuration for a specific element.
Molecular spectra
Atoms and molecules absorb & emit photons of characteristic energy or
frequency, by changing their vibrational modes.
Spectroscopy
•
to monitor car exhausts
•
to find the rotation rate of stars
•
to analyse pigments in a painting
•
to identify forensic substances
•
to map a patient’s internal organs
Photoelectric effect
Observations
• There is a threshold frequency, below which no emission occurs.
• The maximum Ek of the electrons is independent of light intensity.
• Photoelectric current is proportional to light intensity.
Photoelectric effect
Photoelectric effect
Photoelectric effect
Photoelectric effect
Analysis
• Energy of photon E = hf
high energy violet quantum
Electron leaves metal
Electron energy
Quantum energy
Potential well
Work function
(Diagram: resourcefulphysics.org)
• The photon’s energy can do two things:
• enable an electron to escape the metal surface
•
(work function, f).
• give the free electron Ek.
hf  f  E k max
Photon flux
• Calculate the number of quanta of radiation being
emitted by a light source.
• Consider a green 100 W light. For green light the
wavelength is about 6 × 10-7 m and so:
• Energy of a photon = E = hf = hc / λ= 3.3 × 10-19 J
• The number of quanta emitted per second by the
light,
-1
100Js
N
 3 10 s
3.3 10 J
20
19
1
Wave-particle duality
• Reflection, refraction, interference and
diffraction can all be explained by the idea of
light as wave motion. Polarisation also tells us
that the waves are transverse.
• The photoelectric effect means that we have
to attribute some particle properties to light.
• So, which is it?
Wave-particle duality
• We have to use different models to explain
what happens in different situations. Neither
is perfect.
• Louis de Broglie suggested that this same kind
of dual nature must also be applicable to
matter. He proposed that any particle of
momentum (p) has an associated wavelength
λ = h/p = h/mv
Where λ is know as the de Broglie wavelength
de Broglie wavelength of an electron
de Broglie wavelength of an electron
• When you accelerate at about 100V then the
wavelength is of the order of 10-10m. This is of
the same magnitude as an X-ray. We know that
X-rays can diffract because of their wave
properties and so if this were all true and
electrons could exhibit wave behaviour then they
would demonstrate diffraction properties also.
• In 1926 Davison and Germer tried it with a single
nickel crystal. It worked!
Electron diffraction
The double-slit experiment
with electrons
number of electrons
a) 10
b)200
c)6000
d)40 000
e) 140 000
polycrystalline target
(a 2-dimensional grating)
Question Time
• TAP 501-3: Quanta
– (wavelengths, energy and using E =hf)
• Tap 502-2 Photoelectric effect question
– (getting the electron out hf, and giving it some KE, ½ mv2)
• TAP de Broglie worked examples
• TAP 522-6 Electrons measure the size of a nuclei
– (advanced)