Question

The half-life of carbon-$14$ is $5730$ years. Explain how to figure out the age of a substance that has $25\%$ carbon-$14$ remaining?
A) Multiply $25\%$ times $5730$ years since only $25\%$ of the carbon remains.
B) Divide $5730$ years by $2$ since carbon has gone through two half-lives.
C) Multiply $5730$ years by $2$ since two half-lives have gone by for carbon.
D) Multiply $4$ times $5730$ years since carbon has went through $4$ half-lives.

Answer 1

We know that the amount of time takes for a given isotope to lose half of its radioactivity is defined as the half-life period. One can calculate the half-life of an isotope using the formula,
${t_{\left( {\dfrac{1}{2}} \right)}} = \dfrac{{\ln 2}}{k}$
Here, k is the decay constant.
${t_{\left( {\dfrac{1}{2}} \right)}}$- half-life of compound

Complete step by step answer:
We need to remember that the radiocarbon dating is a radiometric dating technique that utilizes $\left( {14C} \right)$ to decide the period of carbonaceous materials up to around $60,000$ years of age. The procedure was created by Willard Libby and his associates in $1949$.
$25\%$means two half-lives. Each half-live takes $5730$ years so in order to find the age of the substance we have to multiply $5730$ years by two.
The age of the substance which has $25\%$ of carbon-14 is $2 \times 5730yrs = 11460yrs$

So, the correct answer is Option A.

Additional information:
We need to remember that one of the incessant employments of carbon dating is to date natural remaining parts from archeological locales. Plants fix environmental carbon during photosynthesis, so the degree of carbon-14 in plants and creatures when they bite the dust roughly approaches the degree of carbon-14 in the air around then. Be that as it may, it diminishes from that point from radioactive rot, permitting the date of death or obsession to be assessed. The underlying carbon-14 level for the figuring can either be assessed, or, more than likely straightforwardly contrasted and known year-by-year information from tree-ring information (dendrochronology) as long as $10,000$ years prior or probably from cavern stores back to around $45,000$ years before the present. A figuring an immediate correlation of carbon-14 levels in an example, with tree rings or cavern stores carbon-14 degrees of a known age, at that point gives the wood or creature test age-since-development. Radiocarbon is additionally used to distinguish aggravation in common environments; for instance, in peatland scenes, radiocarbon can show that carbon which was recently put away in natural soils is being delivered because of land freedom or environmental change.

Note: Scientifically measuring just works for objects that are more youthful than about years and most shakes of interest are more established than years carbon-14 has a half existence of years, implying that after years half of carbon-14 iotas have rotted to nitrogen molecules in a passed on animal types. Essentially, after years just one fourth of unique carbon-14 iotas stay in the dead creatures. Because of the short length of the carbon-14 half-life, scientifically measuring is ideal for issues that are thousands to a huge number of years old.