Question

Isotope Number Number Abundance Half-like

of protons of neutrons (percentage of all
carbon atoms)
Carbon-10 6 4 0 19.29 seconds
Carbon-11 6 5 0 20.33 minutes
Carbon-12 6 6 98.9 (stable)
Carbon-13 6 7 1.1 (stable)
Carbon-14 6 8 Less than 0.1 5730 years
Carbon-15 6 9 0 2.45 seconds
Identifying patterns: describe the pattern in half-ives and abundance shown by the data

Answer 1

The pattern in carbon isotopes shows that stable isotopes like Carbon-12 and Carbon-13 are abundant, while isotopes with more neutrons have shorter half-lives and are less abundant or not found naturally.

Step-by-step explanation:

Isotopes are different forms of the same element with the same number of protons but a different number of neutrons. In the case of carbon isotopes, a pattern in their half-lives and abundance is observed. The more neutrons in the isotope compared to protons, usually the less stable the isotope is, leading to a shorter half-life. Carbon-12 (6 protons, 6 neutrons) is the most abundant and is stable. However, as the number of neutrons increases, like in Carbon-14 (6 protons, 8 neutrons), the stability decreases and the isotope becomes radioactive, leading to a longer half-life but less abundance.

Carbon-12 and Carbon-13 are the only stable isotopes with abundance rates of 98.9% and 1.1% respectively. All other carbon isotopes listed (Carbon-10, Carbon-11, Carbon-14, and Carbon-15) have a 0% abundance rate and are not stable, showcasing short half-lives ranging from few seconds to several thousand years for Carbon-14, which undergoes radioactive decay and is used for the carbon dating technique in archaeology.