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: Convert the half-life from minutes to seconds. The given half-life (T_1/2) is 2 minutes. T_1/2 = 2 \, minutes × 60 \, seconds1 \, minute = 120 \, s Step 2: Use the formula relating half-life and decay constant. The relationship between the half-life (T_1/2) and the decay constant () is given by: T_1/2 = ((2))/() Step 3: Rearrange the formula to solve for the decay constant (). = ((2))/(T_1/2) Step 4: Substitute the values and calculate the decay constant. We know that (2) ≈ 0.693. = (0.693)/(120 \, s) ≈ 0.005775 \, s^-1 Step 5: Express the decay constant in scientific notation and compare with the given options. ≈ 5.775 × 10^-3 \, s^-1 Rounding to two significant figures, we get: ≈ 5.8 × 10^-3 \, s^-1 This matches option D. The decay constant is 5.8 × 10^-3 s^-1.