Transcript Mass and Energy - Beverley High School

Mass and Energy
The unified mass unit
The mass number of a nuclide refers to the number of
protons and nucleons in an atom
1H
7Li
238U
12C etc
• Eg
• However 1 hydrogen nucleus is only approximately
1/238 the mass of a uranium nucleus. This is because
some of the mass is lost as “binding energy” when larger
nuclei form.
• Therefore there is the need to define a unit of mass with
which we can compare the masses of nuclei. This unit of
mass is called the unified mass unit.
The unified mass unit
The unified mass unit is defined as 1/12 of
the mass of a 12C atom.
(Iu = 1.661 x 10-27kg)
The relative atomic mass (Ar) of any atom as
a consequence of this is
Mass of the atom ÷ 1/12 mass of 12C atom
The mass energy relationship
According to the special theory of relativity
mass has an energy equivalent. Any
change in mass corresponds to a change
in energy according to the equation
ΔE = c2Δm
Correspondingly any change in energy corresponds to a change in mass
The energy equivalent of u
Iu = 1.661 x 10-27kg
ΔE = c2Δm
1u = (2.998 x 108)2 x 1.661 x 10-27= 1.499 x10-9J
Equivalently in eV
1.499 109
 932 106 eV
19
1.602 10
i.e. 932MeV
The unit MeV is often used as a measure of mass and this
correctly emphasises the equivalence of mass and energy.
Mass Defect and Binding Energy
• The mass of a nucleus is always less than the
total mass of its constituent nucleons. ( this is
called mass defect)
• This is because the formation of a nucleus
involves the conversion of some of the mass of
the constituents to energy. This is released as
gamma rays. It is called binding energy.
• To separate the components would require the
input of that same amount of energy.
The binding energy of a nucleus is the energy necessary to separate it into its
component nucleons.
Mass of neutrons 2 x 1.008 67u
Mass of protons 2 x 1.007 28u
Mass of He nucleus 4.002 60 u
Mass defect = (2 x 1.008 + 2 x 1.007) – 4.002= 28.3MeV
Binding energy per nucleon
• The binding energy per nucleon of a
nucleus is a measure of the stability of a
nucleus.(This is the binding energy divided
by the mass number.)
• The larger the binding energy per nucleon,
the more stable the nucleus.
The nuclei at the top of the curve are most stable with the largest binding energy
per nucleon. Those to the those nuclei to the left and right have less binding
energy per nucleon
Atoms with low numbers of nucleons can become more stable by
fusing together to become larger nuclei and in the process releasing
binding energy.
Those to the right can achieve stability by becoming less massive by
fission
Fission
A typical fissile material is uranium 235. This process occurs quite
naturally in the material.
If enough nuclei are present (ie the mass is above “critical mass”) the
fusion process becomes an uncontrollable chain reaction.
Fusion provides a much greater increase in binding energy per
nucleon and therefore a much higher energy release per kg.