This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Hey GODS, good to see you again. Step 1: Determine the number of half-lives required. The activity of a radioactive isotope decreases by half with each passing half-life. After 1 half-life, the activity is (1)/(2) of the initial value. After 2 half-lives, the activity is (1)/(2) × (1)/(2) = (1)/(4) of the initial value. After 3 half-lives, the activity is (1)/(2) × (1)/(2) × (1)/(2) = (1)/(8) of the initial value. So, it takes 3 half-lives for the activity to drop to (1)/(8) of its initial value. Alternatively, using the decay formula: (N_t)/(N_0) = ((1)/(2))^n where N_t is the final activity, N_0 is the initial activity, and n is the number of half-lives. We are given (N_t)/(N_0) = (1)/(8). (1)/(8) = ((1)/(2))^n Since (1)/(8) = ((1)/(2))^3, we have n=3. Step 2: Calculate the total time. The half-life of the isotope is 24 minutes. Total time = Number of half-lives × Half-life period Total time = 3 × 24 minutes Total time = 72 minutes The activity will drop to (1)/(8) of its initial value in 72 minutes. This corresponds to option C. The final answer is C. Send me the next one 📸