During an agricultural experiment, a solution containing 1 mole of a radioactive material ( t_ 1/2 = 14.3 days ) was injected into the roots of a plant. The plant was left to settle for 70 hours , after which the activity in its fruit was measured. If the measured activity was 1 Ci , what percentage of the activity is transmitted from the root to the fruit in steady state?

Step-by-step solution

The initial number of radioactive atoms in 1 mole is: N₀ = 6.023 10²³ The decay constant is given by: = 2 t_ 1/2 = 0.693 14.3 24 3600 = 5.61 10⁻⁷ s ⁻¹ The initial activity A₀ of the injected material is: A₀ = N₀ = (5.61 10⁻⁷) (6.023 10²³) = 3.38 10¹⁷ Bq The plant is left to settle for t = 70 hours = 70 24 days = 2.92 days . The total activity of the radioactive material remaining in the plant after this time is: A(t) = A₀ e^ - t = A₀ e^ - 0.693 2.92 14.3 A(t) = 3.38 10¹⁷ e^ -0.141 3.38 10¹⁷ 0.868 = 2.93 10¹⁷ Bq The