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 answer
1/16 = 1/2^x
2^x = 16
Solve for x.
To solve for x, the unknown exponent, we need to find the logarithm base 2 of both sides of the equation.
x = log2(16)
Using the logarithm property logb(n^m) = m * logb(n), we can rewrite log2(16) as:
x = log2(2^4)
Using the fact that 2^4 equals 16, we find:
x = 4
Therefore, the number of half-lives it takes for the amount of the isotope caesium-137 to decay to one sixteenth of its original amount is 4.
Since the half-life of caesium-137 is 30 years, we can calculate the time it takes for 4 half-lives to occur:
Time = 4 * 30 years
Time = 120 years
Therefore, it will take 120 years for the amount of caesium-137 in a sample to decay to one sixteenth of its original amount.