T Mander 2013
Y13 Nuclear Revision
Rev. 18/6/13
Mixing equations
c = fλ
E = hf
E = mc2
Examples: If you know the wavelength you can work out the frequency (c = fλ) which then
allows you to calculate the Energy of a photon (E = hf) and then the mass deficit required to
produce such a photon (E = mc2). Conversely, if you know the mass lost in a nuclear decay you
can work out the total energy released as photons (E = mc2), then their frequency (E = hf),
then their wavelength (c = fλ).
Antimatter
Antimatter particles have the same mass as normal particles but have the opposite charge.
http://en.wikipedia.org/wiki/Antimatter
Antiparticles will annihilate (destroy) normal particles they meet.
The lost mass is released as energy as per E = mc2. The total released energy could be
divided over two or more high energy photons. Their frequency can be then calculated from
E=hf.
Neutron capture
http://en.wikipedia.org/wiki/Neutron_capture
Neutrons can fuse with atoms and create atoms larger than iron (mass 56). Fusion cannot
usually do this because the increasing mass per nucleon (past mass 56) requires the
equivalent amount of energy supplied from somewhere.
The point, however, is that nuclear equations should be balanced. The number of charges and
masses on one side should equal that on the other. If you add a neutron to an atom then that
atom is going to be 1 neutron heavier (unless everything falls apart, and then you call it
fission). This is the same element but an isotope.
Electron volts
eV = Energy
e = -1.6x10-19
Volts times -e = energy in joules
eg. So 1 eV = 1 volt times the negative of -1.6x10-19 = 1.6x10-19 J
Or Energy in Joules ÷ 1.6x10-19 = Energy in eV
T Mander 2013
Possible uses:
Very handy if dealing with the very small energy of very small things. It is a way of talking
about energy on the same scale as electrons.
If given mass of electrons, work out eV.
Photoelectric effect and kinetic energy of an electron, work function, energy and frequency
of incident photon.
eV = Ek = ½ mv2 = hf - ɸ
so hf – Ek = ɸ
Energy Gap
Lyman/Balmer/Paschen
http://www.chemguide.co.uk/atoms/properties/hspectrum.html
There is a minimum energy difference between the different series. The gap between Lyman
and Balmer series is the difference between the smallest drop in Lyman (2 to 1) and the
largest drop in Balmer (free state down to 2).
Photoelectric Effect
T Mander 2013
One assumption of this experiment is that if an electron is fully ejected from the metal then
it will hit the collector plate. The vacuum makes this more likely (stops ionising with the air
and consequent absorption) but a) it’s probably not a perfect vacuum, and b) the electrons
could hit the sides of the tube instead of heading for the collector.
There are two forms of this experiment.
To be emitted from the metal the electron needs to be hit by a photon having a minimum
amount of energy = the work function of the metal. Once it leaves the metal it still might not
reach the collector because of points a and b above. As the energy of the incident photon
increases the likelihood of the electron to have enough energy to get to the collector
increases.
First: In the diagram above the negative terminal of the battery is connected to the
collector.
This means that when there is a current flowing from the emitter the battery voltage is
increased until the current stops. Several readings at different frequencies will enable you
to draw a voltage over frequency graph. Where the graph crosses the x axis shows the
minimum frequency required to generate a current. The y intercept is the work function.
This minimum voltage is the cut-off voltage and is the amount of energy an incident photon
needs in order to get out of the metal. eV = ɸ
Second: The battery can be connected with the positive terminal connected to the collector.
This will mean that emitted electrons will be attracted to the collector instead of going in
another direction and getting absorbed elsewhere. As the voltage from the battery
increases the number of electrons pulled onto the collector increases until all electrons
emitted are also pulled onto the collector.
T Mander 2013
So if you set the voltage so you get all the electrons then reduce the frequency there should
be a clear cut-off frequency when electrons stop being emitted.
A current over voltage graph will go up then flatten off.
http://physics.tutorvista.com/modern-physics/photoelectric-effect.html (note: don’t click
the tutor popup box – it’s not a person).
Other Key Concepts
The photoelectric effect is a central focus of Y13 nuclear physics. It links with E=mc2,
spectral lines, energy levels, mass, and all kinds of things. You need to know everything about
the photoelectric effect.
Binding energy and mass deficit definitions are key to the nuclear topic. Check the main Y13
notes for my own version of them.