An isotope has a half life of 56 days. It now has 10,000DPM/ml. What will its activity be 100 days from now?
To determine the activity of the isotope 100 days from now, we need to understand the concept of half-life and how it affects the decay process. The half-life of an isotope is the time it takes for half of the initial quantity of the isotope to decay.
Given that the half-life of the isotope is 56 days, we can calculate the number of half-lives that will occur in 100 days by dividing the total time (100 days) by the half-life (56 days):
Number of half-lives = Total time / Half-life
Number of half-lives = 100 days / 56 days
Number of half-lives ≈ 1.79
Since we cannot have a fraction of a half-life, we need to consider that after 56 days, one half-life has already completed, leaving us with approximately 0.79 of the second half-life.
To determine the final activity after 100 days, we multiply the initial activity by the fraction of the second half-life left (0.79):
Final activity = Initial activity × (1/2)^Number of half-lives
Final activity = 10,000 DPM/ml × (1/2)^1.79
To calculate (1/2)^1.79, we need to raise 0.5 to the power of 1.79. This can be done using a calculator or by using logarithms. The result is approximately 0.2925.
Final activity ≈ 10,000 DPM/ml × 0.2925
Final activity ≈ 2,925 DPM/ml
Therefore, the activity of the isotope 100 days from now will be approximately 2,925 DPM/ml.