The isotope, Carbon-14 emits beta radiation and has a half live of 5730 years. How long will it take for the amount of radiation this gives off to drop by a factor of 4?
You kidding ?
1/4 = 1/2 * 1/2
so two half lives :)
To determine how long it will take for the amount of radiation emitted by Carbon-14 to drop by a factor of 4, we can use the concept of half-life.
The half-life of Carbon-14 is given as 5730 years. This means that after 5730 years, half of the Carbon-14 atoms will have decayed, and half will remain. After another 5730 years, half of the remaining half will decay, resulting in one-quarter of the original amount remaining, and so on.
To calculate the time it takes for the amount of radiation to drop by a factor of 4, we need to determine how many half-lives are required for this reduction. Since a factor of 4 is equivalent to 2^2 (2 raised to the power of 2), we need to find the number of half-lives it takes for the amount to decrease by a factor of 2 twice.
Each half-life is 5730 years, so we can calculate the time it takes for the amount of radiation to drop by a factor of 4 as follows:
2 * (5730 years) = 11,460 years.
Thus, it will take approximately 11,460 years for the amount of radiation emitted by Carbon-14 to drop by a factor of 4.