Answer:
To determine the half-life of phosphorus, we can use the given information that a 32g sample decayed and only 2g remains undecayed after 60 days. Here's how we can calculate the half-life: 1. Calculate the fraction of the sample remaining after the given time: Remaining fraction = mass remaining / initial mass Remaining fraction = 2g / 32g = 1/16 2. The half-life is the time it takes for half of the sample to decay. Since the remaining fraction is 1/16, we need to determine how many half-lives it takes to reach this fraction. 3. Calculate the number of half-lives: Remaining fraction = (1/2)^(number of half-lives) (1/16) = (1/2)^(number of half-lives) 4. Solve for the number of half-lives by taking the logarithm of both sides of the equation: log[(1/16)] = log[(1/2)^(number of half-lives)] log[(1/16)] = (number of half-lives) * log[(1/2)] 5. Using logarithmic properties, we can rearrange the equation to solve for the number of half-lives: (number of half-lives) = log[(1/16)] / log[(1/2)] 6. Evaluate the expression using a calculator: (number of half-lives) = 4 Therefore, the half-life of phosphorus is 4 days.
Step-by-step explanation: