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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).
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
i) beta minus(electron) particle emitters
ii)beta plus(positron) particle emitters
iii) alpha particle emitters top of curve(not shown)
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
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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