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: Calculate the number of half-lives (n). The number of half-lives is the total time divided by the half-life period. Given: Half-life (T_1/2) = 80 days Total time (t) = 320 days n = (t)/(T_1/2) n = 320 \, days80 \, days n = 4 So, 4 half-lives have passed. Step 2: Calculate the number of atoms remaining (N). The formula for radioactive decay is: N = N_0 ((1)/(2))^n Where: N_0 is the initial number of atoms N is the number of atoms remaining after time t n is the number of half-lives Given: Initial number of atoms (N_0) = 6.0 × 10^10 Number of half-lives (n) = 4 Substitute the values into the formula: N = (6.0 × 10^10) ((1)/(2))^4 N = (6.0 × 10^10) ((1)/(16)) N = 6.0 × 10^1016 N = 0.375 × 10^10 To express this in standard scientific notation, we adjust the decimal: N = 3.75 × 10^9 Step 3: Compare the result with the given options. The calculated number of atoms remaining is 3.75 × 10^9. This matches option A. The number of atoms that would remain at the end of 320 days is 3.75 × 10^9.