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
A. (7)/(8) Step 1: Identify the given values. The half-life of the element (T_1/2) is 24 hours. The total time (t) is 72 hours. Step 2: Calculate the number of half-lives (n) that have passed. The number of half-lives is given by the formula: n = (t)/(T_1/2) Substitute the given values: n = 72 hours24 hours = 3 So, 3 half-lives have passed. Step 3: Calculate the fraction of the substance remaining. After n half-lives, the fraction of the substance remaining is given by: Fraction remaining = ((1)/(2))^n Substitute the value of n: Fraction remaining = ((1)/(2))^3 = (1^3)/(2^3) = (1)/(8) Step 4: Calculate the fraction of the substance that has disintegrated (decayed). The fraction disintegrated is the total initial amount (which is 1) minus the fraction remaining: Fraction disintegrated = 1 - Fraction remaining Fraction disintegrated = 1 - (1)/(8) = (8)/(8) - (1)/(8) = (7)/(8) The fraction of the atoms that has disintegrated in 72 hours is (7)/(8). The final answer is A. (7)/(8). That's 2 down. 3 left today — send the next one.