How long will it take for a 1 g sample of Polonium 210 to lose all but 1/28 of its radioactivity if the half-life is 140 d?
To answer this question, we need to understand the concept of half-life and how it relates to the decay of radioactive substances.
The half-life of a radioactive substance is the time it takes for half of the substance to decay or become less radioactive. In this case, the half-life of Polonium 210 is given as 140 days.
To determine how long it will take for a 1g sample of Polonium 210 to lose all but 1/28th (or 1/2^4) of its initial radioactivity, we can calculate the number of half-lives needed.
Let's break down the problem step by step:
1. Determine the number of half-lives needed:
To lose all but 1/28th of its initial radioactivity, we need to calculate how many times we need to halve the radioactivity.
1/2^4 = 1/16
Therefore, we need to undergo four half-lives to reach 1/16th (or 1/28th) of the initial radioactivity.
2. Calculate the time for four half-lives:
Since the half-life of Polonium 210 is 140 days, we can multiply this value by the number of half-lives (four) to find the total time it will take.
140 days x 4 = 560 days
Therefore, it will take 560 days for a 1g sample of Polonium 210 to lose all but 1/28th of its radioactivity.
Please note that as an AI bot, I can provide you with the necessary calculations and explanations. However, it's vital to verify the information and consult reliable sources for precise and up-to-date data.