C-14 half-life is the time it takes for half of the isotope mass to decay into its daughter form. Line graphs are the best way to represent data about half-lives and the amount of isotope (gr).
Carbon 14, also known as radiocarbon, is a radioactive carbon isotope.
Isotopes are the atoms of the same element -carbon- that vary in neutrons and, hence, in their massic number. They are alternative forms of the same element.
The radioactive C14 nucleus contains 6 protons and 8 neutrons and has a half-life of 5730 years.
The term half-life is a reference. It means that an organism that has been dead for 5730 years has half the C14 amount or concentration than the same organism had when it was alive.
In other words, the half-life is the time it takes for half the mass of this isotope to become its daughter form.
Knowing the half-life of an element is useful to determine the age of the dead matter.
C14 is used in radiocarbon dating techniques or methods to estimate the age of fossils. This is a reliable technique used for dating organic samples that are less than 50,000 years old.
An easy way of representing the change in mass of the isotope through the years is to make a line graph, which is easy to interpret and compare the information.
In this example, our line graph must represent the number of half-lives related to the amount of parent isotope in grams.
The table details the years and the amount of isotope. So, by kowing the half-life of C-14, we can get how many half-lives there are.
5,700 years ---------- 1 half-life
11,400 years--------- X = 2 half-lives ⇒ (5700 x 2) or (11,400/5,700)
17,100 years -------- X = 3 half-lives ⇒ (5700 x 3) or (17,100/5,700)
22,800 years ------ X = 4 half-lives ⇒ (5700 x 4) or (22.800/5,700)
28,500 years ------ X = 5 half-lives ⇒ (5700 x 5) or (28,500/5,700)
34,200 years ------ X = 6 half-lives ⇒ (5700 x 6) or (32,200/5,700)
39,900 years ------ X = 7 half-lives ⇒ (5700 x 7) or (39,900/5,700)
45,600 years ------ X = 8 half-lives ⇒ (5700 x 8) or (45,600/5,700)
51,300 years ------- X = 9 half-lives ⇒ (5700 x 9) or (51,300/5,700)
Now, we can make a new table,
Number of half-lives Carbon-14 (g)
0 ..............................10,000
1 ...............................5,000
2................................2,500
3 ................................1,250
4 ................................ 625
5 ................................ 312
6 ................................ 156
7 ................................. 78
8 ................................. 39
9 ................................. 20
Finally, we can make the line graph using the data of this new table. You will find it in the attached files.
In conclusion, the best graph you can make is a line graph, and if they ask you to graph the number of half-lives and give you the number of years, you can just make the conversion using the half-life of the isotope.
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