The document discusses nuclear stability and radioactive decay. It explains that stable nuclei have a balance of protons and neutrons, while unstable nuclei decay through processes like alpha decay, beta decay, and gamma emission to become more stable. Alpha decay involves emitting a helium nucleus, beta decay changes the number of protons or neutrons by converting between the two, and gamma emission releases energy without changing the nucleus. Unstable nuclei may undergo several types of decay until becoming a stable isotope. The various types of decay are illustrated with nuclear equations and examples.

1. Nuclear Stability and
Radioactive Decay
1

2. Nuclear stability
When a graph of neutron number (N) against proton
number (Z) graph is plotted for all known nuclides – fig 1
is obtained.
2

3. 3
Stable nuclides of lighter elements have ratio N/Z ≈ 1
As Z increases, stability line curves upwards.
Heavier nuclides need more and more neutrons to be
stable. (N/Z ratio ≈ 1.5)
There is an upper limit to the size of a stable nucleus,
because all nuclides with Z higher than 83 are unstable.
Most of the atoms in the world have stable nuclei, but all
nuclei except hydrogen contain at least 2 protons
Positively charged protons repel each other, Coulomb’s
law shows that 2 protons 2 x 10-15 m apart produce a
repulsive force of about 50 N. (electric repulsive force)
So why does the nucleus not blow apart?

4. 4
Another force acts between nucleons – strong nuclear
force. (100 times stronger than the electric repulsive
force).
Strong nuclear force is attractive over short distances
(0.5 x 10-15 m) and so holds the nucleons together.
In stable nuclei these forces hold the nucleons together
as they are balanced, imbalance makes nuclei unstable.
Atoms of radioactive materials have unstable nuclei and
decay to become more stable by emitting radiation in one
or more of the following ways:
1. Alpha decay (α)
2. Beta minus decay (β-)
3. Beta plus (positron) emission (β+)
4. Electron capture
5. Isometric transition or gamma decay (γ)

5. 5
A nuclide may undergo several decays before it becomes
stable – called a decay chain.
Parent nuclide – the nuclide at the beginning of a
particular decay chain.
Daughter nuclide – new nuclide produced by decay (may
or may not be stable).
Alpha decay
An alpha-particle is a helium nucleus and is written as 4
2α
or 4
2He – consists of 2 protons and 2 neutrons.
This decay can be represented by a nuclear equation:
A
ZX → A-4
Z-2X + 4
2α
Notice that the top and bottom numbers balance on each
side of the equation.
Often followed by gamma ray and sometimes a
characteristic X-ray emission.

6. 6
An α particle is emitted in the decay of many elements with
a proton number greater than lead (Z › 82)
Polonium-208 emits an alpha particle and becomes an
isotope of lead:
208
84Po → 204
82Pb + 4
2α
Every decay releases 5.1 MeV of energy – KE of the
ejected α-particle (majority) and recoil of the daughter
nuclide
Nearly all α-emitters eject most of their alpha particles
with a single energy value (energy value is characteristic of
the nuclide)

7. Beta decay
7
Emitted by nuclides with an excess of neutrons over
protons.
This is the emission of an electron from the nucleus – but
there are no electrons in the nucleus!
One of the neutrons changes into a proton (remains in
nucleus) and an electron (emitted as β- particle)
So proton number (Z) increases by one, but nucleon number
(A) remains the same and is represented by the nuclear
equation:
A
ZX → A
Z+1X + 0
-1β
Platinum-199 changes to gold-199 by β-decay
199
78Pt → 199
79Au + 0
-1β

8. 8
Each decay of a Pt-199 nucleus releases 1.8 MeV of
energy – might expect it to appear as KE of β-particles.
This does not happen as emitted β-particles have a range
of KEs – see graph on the board.
Wolfgang Pauli (1930) suggested another particle is also
emitted during the decay (antineutrino) – KE shared
between electron and the antineutrino. (discovered 1956)
The antineutrino (antimatter particle) has no charge and
no mass – decay equation then becomes:
199
78Pt → 199
79Au + 0
-1β + 0
0ν¯
All β-emitters produce β-particles with a range of
energies up to a maximum value – this value is
characteristic of the nuclide.

9. Gamma-emission
9
Gamma-emission results in no change in the structure of
the nucleus, but makes the nucleus more stable –
reduces energy of the nucleus.
A nucleus that emits an α-particle or β- particle often
left in an excited state – losing surplus energy by
emitting a γ-ray photon.
Aluminium-29 changes to
silicon-29 by β-emission, and
then a γ-photon of energy
1.4 MeV
29
13Al
29
14Si
29
14Si
β¯
γ
2.5 MeV
1.4 MeV
Energy, hence wavelength of the γ-ray emitted is
characteristic of that nuclide

10. Beta+ decay
10
A radio-nuclide above the stability line (see fig 1 slide 2)
decays by β-emission (slide 7) – moves diagonally
towards the stability band.
Radio-nuclides below the stability line undergo positron-
decay (β+ decay) to move diagonally towards stability
band)
Positron is the antiparticle of the electron – same mass
but opposite charge, represented as 0
+1β or 0
+1e
A proton in the unstable nucleus changes into a neutron
and a positron – neutron remains, positron is ejected.
General equation is:
A
ZX → A
Z-1X + 0
+1β + ν

11. 11
A second particle, the neutrino v, is emitted with the
positron – it is a massless, chargless particle.
Notice, as always, top and bottom numbers balance.
Positrons emitted by unstable nuclei which have a deficit
of neutrons compared to protons
Compare the following two decays:
14
6C → 14
7N + 0
-1β + 0
0ν¯
15
8O → 14
7N + 0
+1β + ν
Electron Capture
In this type of nuclear change, a proton combines with an
electron from an inner shell – usually the n = 1 shell
Results in the production of a neutron – has the same
effect on the nucleus as β+ decay (reducing Z by 1) as
electron combines with a proton.

12. 12
Subsequently an electron will move from an outer shell to
fill the space left by captured electron.
Results in a characteristic X-ray photon being emitted.
An example is the decay of Cr-51 to V-51 with a
neutrino.
51
24Cr + 0
-1e → 51
23V + 0
0v + X-ray
Energy is carried away by the neutrino and the X-ray
photon.
Decay chains
A radio-nuclide often produces an unstable daughter
nuclide – this will also decay and process continues until a
stable nuclide is produced.
Called a decay chain (or decay series) – the uranium-238
decay chain is shown on the next slide.

13. 13
238
92U 234
90Th + 4
2α 234
91Pa + 0
-1β
234
92U + 0
-1β230
90Th + 4
2α226
88Ra + 4
2α
222
86Rn + 4
2α 218
84Po + 4
2α
214
82Pb + 4
2α
214
83Bi + 0
-1β214
84Po + 0
-1β
210
82Pb + 4
2α
210
83Bi + 0
-1β 210
84Po + 0
-1β 206
82Pb + 4
2α
Lead-206 is a stable isotope

14. Questions
1. Z number for Pb =82, F = 9 and Fe =
26. Write nuclear equations for the
following decays:
(a)Beta-emission from oxygen-19 (19
8O)
(b)Alpha-emission from polonium-212
(212
84Po)
(c)Positron-emission from cobalt-56
(56
27Co)
14