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Stability: the N-Z curve

[the N-Z curve][decay chains]

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 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

• 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).