Final answer:
The correct phrase regarding the ratio of stable carbon isotopes is that the carbon-12 to carbon-13 ratio can provide information on diet and metabolic processes. Carbon-12, which is not radioactive, is more abundant in nature and living organisms than carbon-13.
Step-by-step explanation:
Among the phrases about the ratio of different stable isotopes of carbon, option c is correct: The ratio of carbon-12 to carbon-13 can provide information about diet and metabolic processes. This is because different sources of carbon in nature (such as different types of plants) have varying ratios of carbon-12 (¹²C) and carbon-13 (¹³C), which can be reflected in the tissues of organisms that consume these plants. Thus, analyzing the ratio can give us insights into the diet and metabolism of an organism.
However, option a is incorrect; carbon-12 is not radioactive. It is a stable isotope with six protons and six neutrons in its nucleus. The radioactive isotope of carbon is carbon-14 (¹⁴C), which is used in radiocarbon dating to determine the age of organic materials.
Option b is also incorrect; carbon-12 is more abundant in nature compared to carbon-13. The abundance of carbon-12 in living organisms and in the carbon cycle makes it a primary isotope in biological systems. Lastly, option d correctly states that carbon-12 is always more abundant than carbon-13 in living organisms.