q983002
Discuss the connection between natural radioactivity and Einstein’s famous
mass/energy equation.
Try HSC 2012: Question 34
Check your answer by reviewing the solution guidelines on the next page.
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Solution Guidelines
(The solution is more detailed than required in a H.S.C. answer. The
solution is designed to give your greater depth of knowledge in
preparation of your H.S.C. Physics examination)
There are three kinds of natural radiations, alpha particles , beta particles  and
gamma rays  that are emitted from a nucleus of an unstable atom.
An alpha particle ( particle) is a helium nucleus 4He2 that is naturally emitted from an
unstable nucleus producing a nucleus of a new element.
Emission of a 4He2 nucleus: N → (N – 2)
Z → (Z – 2)
A → (A – 4)
Transmutation of a parent P into its daughter D:
A
PZ 
A-4
DZ-2 + 4He2
Example
radium
 random + 
226

Ra88
222
Rn86
136 n
86 p
138 n
88 p
2n
2p
+ 4He2
Mass (parent) > Mass (products)
Mass defect m = Mass(parent) – Mass(products)
Kinetic energy of products is due to the mass defect (from E = m c2)
KE(products) = m c2
Beta decay: when a nucleus exists which has either too many or too few neutrons
relative to the number of protons present for stability. Stability can be achieved by the
conversion inside the nucleus of a proton into a neutron or a neutron into a proton. In
this transmutation:
Charge is conserved  a beta particle (+ or -) is emitted from the nucleus
Energy and momentum are conserved 
a particle called a neutrino (e or  e ) must also be emitted from the nucleus.
Greek letter nu ()
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Reduction of a neutrons & increase in a proton inside nucleus
n  p  e   e
N → N–1
A
PZ 
14
C6 
A
N / Z too large
e   
Z → Z+1
A→A
DZ+1 + e- +  e
14
N7 + e- +  e
Mass (parent) > Mass (products)
Mass defect m = Mass(parent) – Mass(products)
Kinetic energy of products is due to the mass defect (from E = m c2)
KE(products) = m c2
Gamma rays ( rays) are photons having very high energy that were emitted from
excited nuclei, much like emission of photons by excited atoms. Like an atom, a
nucleus itself can be in an excited state. When it jumps down to a lower energy state it
emits a photon called a  ray. The energy level separations in a nucleus (~ MeV) are
much greater than the energy level differences in an atom (~ eV). For a given decay,
the  ray always has the same energy and since the photon is electrically neutral, there
is no change in the element as a result of the decay.


Gamma rays are extremely high frequency (short wavelength) electromagnetic
waves where the photons are emitted from excited nuclei.
N, Z and A do not change
222
222
86 Rn*  86 Rn  
A nucleus can be in an excited state after it suffers a violent collision with another
particle, or more commonly the daughter nucleus remaining after an  decay or 
decay is left in an excited state.
226
Ra88
222

Rn86* 
222
Rn86* + 4He2
222
Rn86 + 
energy of  particle 4.685 MeV
energy of  ray 0.186 MeV
The energy of the emitted gamma ray is due to the decrease in mass in the gamma
emission process: mass  energy as given by E = m c2
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