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**NUCLEAR PHYSICS**

**Stability: the N-Z curve**

the N-Z curve |

__The N-Z curve __

The N-Z curve is a plot of the number of neutrons(N) against the number of protons(Z).

**lines**:

i) the 'stability' line - a gentle curve starting from the origin and of increasing gradient

ii) the line of N = Z - a straight line of gradient '1' through the origin

**regions**

i) beta minus(electron) particle emitters

ii)beta plus(positron) particle emitters

iii) alpha particle emitters top of curve(not shown)

**description**:

For proton numbers(Z) up to 20, N=Z is a straight line.

For all nuclei with Z>20 , stable nuclei have more neutrons than protons, the line curves upwards.

Unstable nuclei __above__ the stability curve are called **neutron-rich**.

Unstable nuclei __below__ the stability curve are called **neutron-poor**.

__The Decay Process__

Unstable neutron-rich nuclei can become more stable by __losing__ neutrons. They do this by '**beta decay**'.

The effect of this for a single nucleus is to __raise__ its the proton number (Z) by 1 and decrease its neutron number(N) by 1, bringing the N-Z plot of the nucleus closer to the stability curve.

The movement of the point is right one unit and down one unit.

**beta decay: Z + 1 N - 1 **

Unstable neutron-poor nuclei can become more stable by __gaining__ neutrons. They do this by '**positron decay**'.

The effect of this for a single nucleus is to __lower__ its proton number (Z) by 1 and increase its neutron number(N) by 1 , bringing N-Z plot of the nucleus closer to the stability curve.

The movement of the point is left one unit and up one unit.

**positron decay: Z - 1 N + 1 **

**Alpha decay** has very little effect on the position of a nucleus relative to the stability curve. This is is because the loss of an alpha particle(2 protons + 2 neutrons)does not upset the N-Z ratio too much.

The point representing a nucleus has Z - 2 and N - 2 . Only large nuclei participate in alpha decay. So the effect is only confined to the very top section of the curve.

**alpha decay: Z - 2 N - 2**

__Decay Chains__

A **decay chain** (or** radioactive series**) charts the different types of radioactive decay a nucleus undergoes until a stable isotope is reached.

There are only 3 naturally occuring decay chains called the:

**actinium series**, ** thorium series**, **uranium series**,

plus one other involving a trans-uranium element, the **neptunium series**.

A decay chain is accurately described using a graph of nucleon number(A) against proton number(Z).

The graph illustrates the complete Thorium-232 decay chain.

click on image to magnify (in pop-out page)

Important observations are:

alpha decay ...........2 units to the left, 4 units down

beta^{-} decay ...........1 unit to the right

Bismuth ...............2 possible decay outcomes

Equations describing the Thorium Series:

. . . etc.

As an exercise, it is left to the reader to complete the series using the decay chain graph(above).

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