Respuesta :
Answer:
The answer is "4,241 .17 years"
Explanation:
The disintegration rate, which shows in C-14 atoms = [tex]15.3 \frac{atoms}{min-g}[/tex]
Rate of sample disintegration =[tex]9.16 \frac{atoms} {min-gram}[/tex]
The digit proportion of C-14 can be determined that is included in the sample [tex]= \frac {9.16}{15.3} \\\\ = 0.5987[/tex]
5730 years from half-life.
The number with half-lives (n) which are repelled must be determined:
[tex](\frac{1}{2})^n= A\\\\A= fraction of C-14, which is remaining \\\\(\frac{1}{2})^n= 0.5987 \\\\ n \log 2 = - \log 0.5987\\\\[/tex]
[tex]\therefore \\\\ \Rightarrow n= \frac{0.227}{0.3010} \\\\ = 0.740\\[/tex]
So, the age of the sample is given by = [tex]n \times\ half-life[/tex]
[tex]= 0.740 \times 5730 \ years \\\\=4241.17 \ years\\\\[/tex]
Rate of disintegration is defined as the time required by a sample or substance at which half of the radioactive substance disintegrates. It depends on the nature of disintegration and amount of substance.
The age of the sample is approximately 4241.17 years.
Given that:
C-14 atoms disintegration rates = 15.3 atom/ min-g
Rate of disintegration of the sample = 9.16 atom/ min-g
The digit proportion of carbon-14 is = [tex]\dfrac{9.16}{15.3}[/tex] = 0.5987
Now, also the half-life of carbon-14 is 5730 years.
Such that:
[tex]\dfrac{1}{2}^n = \text A[/tex]
[tex]\dfrac{1}{2} = 0.5987[/tex]
Taking log:
n log 2 = -log 0.5987
Thus, n = [tex]\dfrac{0.227}{0.3010}[/tex]
n = 0.740
The age of the sample can be given by:
Age = n x half-life
Age = 0.740 x 5730
Age = 4241.17 years.
Therefore, the age of the substance is 4241.17 years.
To know more about disintegration rate, refer to the following link:
https://brainly.com/question/14021442
