On Monday you helped me to understand and answer the one question, but I am not too sure if they want all the calculations that you answered... regretably, I am still a bit lost with these!
Below is the question as it is printed:
The isotope caesium-137, which has a half-life of 30 years, is a product of nuclear power plants. How long will it take for the amount of this isotope in a sample of caesium to decay to one-sixteenth of its original amount? Explain your answer. (A few sentences)
.......... the reason why I think I do not need the calculations is because it asks for a FEW SENTENCES, am I right in my thinking? If so, can you pls help me with what I should write?
If I remember the problem right, I think I worked it incorrectly ( that is I don't remember how I worked it but I seem to remember an answer of 40+ years). I don't know what went wrong, assuming I remember correctly. The correct answer is 120 years.
It will take 30 years for 1/2 of Cs-137 to decay (leaving 1/2), 60 years for 1/2 of that to decay (leaving 1/4), 90 years for 1/2 of the 1/4 to decay (leaving 1/8), and 120 years for 1/2 of the 1/8 to decay (leaving 1/16).
To answer the question, you can explain the concept of half-life and how it relates to the decay of the isotope caesium-137. Start by mentioning that the half-life of caesium-137 is 30 years, which means that it takes 30 years for half of the isotope in a sample to decay.
Next, explain that since we want to find out how long it will take for the amount of caesium-137 to decay to one-sixteenth of its original amount, we need to consider the number of half-lives it would take to reach this point.
Each half-life reduces the amount of caesium-137 by half. So, it would take one half-life (30 years) for the amount to be reduced by half, leaving 1/2 of the original amount.
To further reduce the amount to 1/4, we need to go through another half-life. This means an additional 30 years, making it a total of 60 years.
Similarly, for the amount to reach 1/8, we need to go through another half-life, which would take a total of 90 years (30 years for each half-life).
Finally, to reach 1/16 of the original amount, we need to go through another half-life, making the total time 120 years (30 years for each half-life).
In summary, it will take 120 years for the amount of caesium-137 in a sample to decay to one-sixteenth of its original amount, based on the understanding that each half-life reduces the amount by half.