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Nuclear Stability and Radioactive Decay

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

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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 protonsPositively 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?

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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 capture5. Isometric transition or gamma decay (γ)

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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 decayAn alpha-particle is a helium nucleus and is written as 4

2α or 42He – consists of 2 protons and 2 neutrons.

This decay can be represented by a nuclear equation:A

ZX → A-4Z-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.

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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 → 20482Pb + 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)

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Beta decayEmitted 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:

AZX → A

Z+1X + 0-1β

Platinum-199 changes to gold-199 by β-decay199

78Pt → 19979Au + 0

-1β

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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 → 19979Au + 0

-1β + 00ν¯

All β-emitters produce β-particles with a range of energies up to a maximum value – this value is characteristic of the nuclide.

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Gamma-emissionGamma-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

2913Al

2914Si

2914Si

β¯

γ

2.5 MeV

1.4 MeV

Energy, hence wavelength of the γ-ray emitted is characteristic of that nuclide

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Beta+ decayA 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

+1eA proton in the unstable nucleus changes into a neutron and a positron – neutron remains, positron is ejected.General equation is:

AZX → A

Z-1X + 0+1β + ν

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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 → 147N + 0

-1β + 00ν¯

158O → 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.

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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 + 00v + 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.

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23892U 234

90Th + 42α 234

91Pa + 0-1β

23492U + 0

-1β23090Th + 4

2α22688Ra +

42α

22286Rn + 4

2α 21884Po +

42α

21482Pb + 4

2α

21483Bi + 0

-1β21484Po + 0

-1β210

82Pb + 4

2α

21083Bi + 0

-

1β210

84Po + 0-

1β206

82Pb + 42α

Lead-206 is a stable isotope

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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 (198O)

(b)Alpha-emission from polonium-212 (212

84Po)

(c)Positron-emission from cobalt-56 (56

27Co)