Radioactive Decay

1
Radioactive Decay

• The nuclei of some chemical elements are unstable
  against the strong nuclear force holding them
  together, resulting in a spontaneous change of
  characteristic or identity of the element.
• This is especially common for elements above 92
• There are 3 methods of decay

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Decay Mechanisims

• ? - decay
• ? - decay
• ? - decay

• A Helium nucleus seems to emerge from the
  unstable element
• An electron and neutrino emerge from the unstable
  element
• A photon emerges from the unstable element

3
? - decay

• Helium nucleus emerges from the unstable element.
• 92 238U ? 90234Th 24He energy
• electric repulsion becomes greater than the
  nuclear attraction/ contrast between short and
  long range forces.
• Masses do not balance! Why?

4
? - decay

• An electron and a neutrino emerge from the
  unstable nucleus.
• 614C ? 714N - 10e energy
• Weak force - a down quark in a neutron changes
  into an up quark changing it into a proton.
• Masses do not balance! Why?

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? - decay

• Photon emerges from the unstable element
• The element retains its identity
• 13 27 Al ? 13 27 Al ? energy
• nucleus is not changed but has an excess of
  energy - particles are agitated and farther away
  from each other.
• Masses dont balance!

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Masses dont balance!

• Einstein - mass IS energy
• E ?mc2
• ?m is the mass difference between the parent
  nuclei and the daughters. The equation gives the
  energy released. Mass is converted into energy!

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Decay Process

• The fraction of atoms decaying in a time interval
  ?t is
• The value of ? depends on the nucleus
• The unit of ? is 1/seconds (per second)

• ?N / N -? ?t

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Decay Measurement In the LabMeasuring ? for an
element Villanovium

• ?N / N -? ?t

2. Timer for Geiger Counter
Vu
3. Count decay particles during time interval
1. How may atoms of Villanovium?
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The Decay Equation

• The fraction of atoms decaying in a time interval
  ?t is
• Using calculus on this equation, we get
• N(t) - at time t N0 - at beginningt -
  elapsed timee 2.71828

?N / N -? ?t
N(t) / N0 e -?t
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Decay Equation how it works
N(t) / N0 e -?t

• How does N(t) decrease with time?

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ADD a fraction each time compound interest
N(t) / N0 e ?t
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Decay Equation how it works
N(t) / N0 e -?t

• Suppose 10 decays each second

50, half-life ?
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Half-Life when ½ remains
N(t) / N0 e -?t

• Half-life t½ when 10 decays in a second ---
  about 6.4 seconds

NEVER REACHES 0
Seconds
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If you know ? , you can find t1/2

• Suppose that 50 is left, then
• Since we know ? we can solve for t1/2. We call
  that time the half-life how long it takes (in
  seconds) for ½ of the sample to decay.

N(t) / N0 e -?t 0.5
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Half-life examples