Radioactive Decay

1
Radioactive Decay

• Isotopes an element having different atomic
  masses. (same number of protons but different
  number of neutrons)
• All isotopes therefore have same chemical
  properties. (since chemical reactions depend on
  the pattern of electrons around the atom)

2
Radioactive Decay

• A radioactive Nucleus is defined as an unstable
  assembly of neutrons and protons
• Stability is achieved by emitting a radioactive
  particle or a ? photon and is termed radioactive
  disintegration.
• Nuclei emitting ? or ? particles change their
  identity to become different isotopes which can
  also be radioactive and further disintegrate.
• The disintegration series ends when a non
  radioactive product results.

3
Radioactive Changes

• ? - fast moving particle with a mass about the
  same as the helium atom. Hence composed of 2
  neutrons and two protons with a resultant charge
  of 2.

4
Radioactive Changes

• ? - fast moving electrons emitted with high
  energy produced by the nucleus. i.e. ? emission
  occurs when a neutron in the nucleus becomes a
  proton.
• total charge after emission must be equal to
  total charge before.

5
Radioactive Changes

• ? - emission. A ? photon carries no charge or
  mass. It takes energy away from the nucleus
  without altering composition.
• I.e it does not produce a new isotope
• photons are particles released composing of
  light and other forms of electromagnetic
  radiation.

6
Exponential Decay

• If we start with a radioactive isotope X
  containing a number of atoms that decrease as
  individual nuclei disintegrate to form another
  isotope so the mass of X decreases, which
  measurements show to be exponentially.
• Example. If 100? g of isotope X after a time t1,
  the mass of X has fallen to 80? g through decay.
  Then it will decrease to 80 of 80? g in a
  further increment of t1 again.
• The half Life is a measurement used for simple
  convenient reference. It is essentially the time
  taken for the number of atoms of that isotope to
  decrease by half the initial number.

7

8
Worked Example

• Radio active decay is based on the assumption
  that the disintegrations are entirely random so
  how can we explain exponential decreases.
• Class Exercise.
• Exponential A function which raises some
  given constant

9
Summary

• If we start with No of atoms of radioactive
  isotope X
• and let the number of atoms of X remaining in
  time t be N
• In a short interval of time ?t, suppose ?N atoms
  disintegrate.
• Since the process is entirely random, ?N is
• proportional to N, atoms still to disintegrate
• proportional to ?t, the short interval of time
• We can therefore write ?N in terms of a constant
  of proportionality ? (called the decay constant)
• ?N -?N ?t
• Activity is therefore ?N (number of
  disintegrations)
• ?t (time interval)
• Hence. ?N - ?N
• ?t