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
Step 1: Identify the given values. From the image, we have: • Total time elapsed (t) = 24 days • Initial mass (N_0) = 64 g • Final mass (N) = 2 g • We need to find the half-life (T_1/2). Step 2: Calculate the number of half-lives (n). The formula for radioactive decay is: N = N_0 ((1)/(2))^n Substitute the given values: 2 g = 64 g ((1)/(2))^n Divide both sides by 64 g: (2)/(64) = ((1)/(2))^n (1)/(32) = ((1)/(2))^n Since 2^5 = 32, we can write (1)/(32) as ((1)/(2))^5. ((1)/(2))^5 = ((1)/(2))^n Therefore, the number of half-lives (n) is 5. Step 3: Calculate the half-life (T_1/2). The total time elapsed (t) is the product of the number of half-lives (n) and the half-life period (T_1/2): t = n × T_1/2 Substitute the known values: 24 days = 5 × T_1/2 Now, solve for T_1/2: T_1/2 = 24 days5 T_1/2 = 4.8 days The final answer is 4.8 days. Send me the next one 📸