Final answer:
The decay constant for a radioactive source that starts with 14000 Bq activity and decreases to 4000 Bq in 100 seconds is approximately 0.01352 s-1.
Step-by-step explanation:
The decay of a radioactive substance is described by the equation R = R°e−λt, where R is the activity at time t, R° is the initial activity, e is the base of natural logarithms, and λ is the decay constant. To find the decay constant, we will arrange the formula to solve for λ:
λ = -ln(R/R°) / t
Given an initial activity R° of 14000 Bq and a reduced activity R of 4000 Bq after 100 seconds, we can calculate the decay constant (λ) as follows:
λ = -ln(4000 Bq / 14000 Bq) / 100 s
λ = -ln(0.2857) / 100 s
λ ≈ 0.01352 s-1 (result rounded to five decimal places)