ACTIVITY OF NUCLEAR RADIATION

Activity, measured in bequerels Bq ( disintegrations per second ) depends on two things only!

• How many atoms of the isotope you have
• What isotope you have - a very unstable isotope will have a short half life so will be very active!

Activity is NOT the same as count rate of a detector. No detector is 100% efficient, count rates depend on distance from the source, and no counter can capture all emissions - not the least because of internal absorption in the source if solid.

( Think in terms of something silly - knowingly walking off with a radioactive source in your pocket. The inherent danger to you will depend on - isotope type and mass present - number of atoms.)

ACTIVITY is proportional to NUMBER OF ATOMS

A = l N

l = DECAY CONSTANT, a number unique to each isotope = 0.693 / T_1/2 unit of l is s^-1
(derivation next web page)

GRAPHICALLY Activity = - slope of graph (nuclei remaining ~ time) = - dN/dt = - rate of change of number of nuclei

The activity equation is very important. We can use it to measure extremely long half lives eg U-238. Simply take a very pure known mass sample of the isotope and measure its activity. We can also use it to predict the mass of a known activity of isotope - essential in medicinal applications.

eg; How many grams of Co-60 ( half life = 3.65 yr ) will have an activity of 3.7 x 10⁹ Bq ( 100 mCurie )? ( The obsolete unit, the Curie,Ci, was the activity of 1 gram of radium-226 )

Solution; The activity is in units of Bq, ie disintegrations s^-1 thus we must convert 3.65 yr to seconds and find the Decay Constant.

l = 0.693 / 3.65 x 365 x 24 x 3600

N = number of nuclei = A / l = 3.7 x 10⁹ x 3.65 x 365 x 24 x 3600 / 0.693 = 4.26 x 10¹⁷ /0.693

= 6.15 x 10¹⁷ nuclei

Using Avogadro's number and the relative mass of 60,

number of moles = 6.15 x 10¹⁷ / 6.03 x 10²³ = 1.02 x 10^-6 mol

thus mass = 6.13 x 10^-5 grams