The decay constant,k,is given for each of the beta emitters below.Which one has the shortest half life? A).¹¹⁵In,4.29 × 10^-⁹ s^-1 B).¹³¹I,9.94 × 10^-7 s^-1 C).²¹⁷At,21.4 s^-1 D).⁴²K,1.55 × 10^-⁵s^-1

Question

Quizplus · Accepted Answer

The half-life of a radioactive material is inversely proportional to its decay constant (λ) which is given by:
λ = ln(2) / T1/2
where T1/2 is the half-life. 
Thus, the smaller the decay constant, the longer the half-life. 
Comparing the given decay constants, we see that option C has the largest value of λ, which means it has the smallest half-life. Thus, option C has the shortest half-life among the given options.

The Decay Constant,k,is Given for Each of the Beta Emitters