Question

Radioisotopes are often used in medical imaging, however are not something we want to linger in the body for very long. Therefore, we try to use ones that decay quickly. One radioisotope, 18F, has a half-life of 109 minutes.

What is the rate constant for this reaction (in min-1)? 18F is not specifically reacting with anything, but is decomposing into something not radioactive.

Answer 1

We, know that radioactive decay reactions are first order reactions. So is the decay of radioisotope 18F.

Half life or T_1/2 is the time required for a radioactive reactant to reach 50% of its initial concentration or fall to half of its initial concentration.

The half life of first order reactions is independent of the concentration of the reactants, and is solely dependent on the rate constant.

The Half life of a first order reaction is:

• 
  • Here, T_1/2 is the rate constant (min)
  • Ln 2 = 0.693
  • K is the rate constant.(min ^-1)

Thus, the rate constant can be obtained by dividing ln 2 by the half life:

• 
• Putting values we get,
• K = 0.693/109 min^-1
• 6.3 x 10³ min^-1