Ch. 5.4 Half-Life of a Radioisotope

Half-Life

  • The half-life of a radioisotope is the time for the radiation level to decrease (decay) to one half of the original value. This also means that one-half of the amount of the original isotope remains

Decay Curves

  • The decay curve illustrates the amount of time that is required for one half of the substance to be converted into a different element

  • Half-life is the time required for the radiation level (or quantity of a radioisotope) to decay to one-half of its original value.

Half-Life Calculations

STEP 1

  • state the given and needed qualities

STEP 2

  • write a plan to calculate the unknown quantity

STEP 3

  • write the half-life equality and conversion factors

STEP 4

  • set up the problem to calculate the needed quantity

Quick Formulas to Remember

  • Number of half-lives elapsed: n = rac{t}{t_{1/2}}

  • Remaining quantity after time t: N(t) = N0 imes 2^{-n} = rac{N0}{2^n}

  • General continuous form (alternative): N(t) = N0 imes iggl( rac{1}{2}iggr)^{ rac{t}{t{1/2}}} = N0 imes e^{- rac{t \, ext{ln}(2)}{t{1/2}}}

  • Practical interpretation: each full half-life halves the remaining amount; fractions of half-lives reduce accordingly.

Suppose you had a 10.00 grams radioactive element that had a 1/2 life of 3.00 minutes. How long would it take to get to less than 1 gram?

time (min)        amount (g)

0                         10.00

3                            5.00

6                            2.50

9                            1.25

12                          0.675

It would take 12 minutes.  Or 4 half lives.