This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Determine the fraction of the original atoms remaining. The problem states that the radioactive element decayed to (1)/(8) of its original atoms. This means the fraction remaining (N/N_0) is (1)/(8). Step 2: Calculate the number of half-lives (n). The formula for radioactive decay is: (N)/(N_0) = ((1)/(2))^n Substitute the given fraction: (1)/(8) = ((1)/(2))^n Since 2^3 = 8, we can write (1)/(8) as ((1)/(2))^3. ((1)/(2))^3 = ((1)/(2))^n Therefore, the number of half-lives (n) is 3. Step 3: Calculate the half-life (T_1/2). The total time elapsed (t) is given as 6 minutes. The relationship between total time, number of half-lives, and half-life period is: t = n × T_1/2 Substitute the known values: 6 minutes = 3 × T_1/2 Now, solve for T_1/2: T_1/2 = 6 minutes3 T_1/2 = 2 minutes The final answer is 2 minutes. 3 done, 2 left today. You're making progress.