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 Joy — ready when you are. Step 1: Determine the fraction of the original atoms remaining. The problem states that the element will lose (31)/(32) of its original atoms. The fraction of atoms remaining is: 1 - (31)/(32) = (32)/(32) - (31)/(32) = (1)/(32) Step 2: Relate the fraction remaining to the number of half-lives. The formula for the fraction of a radioactive substance remaining after n half-lives is: (N)/(N_0) = ((1)/(2))^n Where (N)/(N_0) is the fraction remaining, and n is the number of half-lives. Step 3: Calculate the number of half-lives (n). Substitute the fraction remaining into the formula: (1)/(32) = ((1)/(2))^n We know that 2^5 = 32. So, (1)/(32) = ((1)/(2))^5. Therefore, n = 5. This means 5 half-lives have passed. Step 4: Calculate the total time taken. The half-life (T_1/2) of the element is given as 7 years. The total time (T) is the number of half-lives multiplied by the half-life period: T = n × T_1/2 T = 5 × 7 years T = 35 years The final answer is D. Send me the next one 📸