Question

\(\begin{array}{l}{\text { The amount of carbon-14 in ancient artifacts and fossils is often used to }} \\ {\text { establish their age. Determine the number of protons and the number of }} \\ {\text { neutrons in a carbon-14 isotope and write its symbol in the form } \frac{A}{Z} \mathrm{X} \text { . }}\end{array}\)

Short answer

Carbon-14 has 6 protons and 8 neutrons, and its symbol is \( \frac{14}{6} \mathrm{C} \).

Step-by-step solution

Understanding Carbon-14

Carbon-14, also known as radiocarbon, is an isotope of carbon. Its notation includes the element symbol (C for carbon), the atomic number (Z), which is the number of protons, and the mass number (A), which is the sum of protons and neutrons in the nucleus.

Determine the Number of Protons

For all carbon isotopes, the number of protons is 6. This is because the number of protons defines the element, and the element of carbon always has 6 protons. Hence, in carbon-14, Z = 6.

Calculate the Number of Neutrons

To find the number of neutrons, subtract the number of protons (Z) from the mass number (A). For carbon-14, the mass number A is 14. So, the number of neutrons = A - Z = 14 - 6 = 8.

Write the Isotope Symbol

With Z = 6 and A = 14, the isotope symbol for carbon-14 can be written using the notation \( \frac{A}{Z} \mathrm{X} \), which translates to \( \frac{14}{6} \mathrm{C} \).

Key concepts

Isotopes

Isotopes are versions of elements that have the same atomic number but differ in the number of neutrons within their nuclei. The atomic number, which represents the number of protons, remains constant for a given element, ensuring its chemical properties are preserved. Each isotope of an element has its unique set of characteristics attributable to the variation in the neutron count.

For example, carbon-14 is one of the isotopes of carbon, distinct from the more common carbon-12, due to its two extra neutrons. These additional neutrons result in a heavier nucleus and lead to different stability characteristics, which is the crux for methods such as radiocarbon dating.

Despite the differences in mass number, all carbon isotopes still behave chemically as carbon because their electron configuration, dictated by the atomic number, remains unchanged.

Atomic Number

The atomic number is a fundamental property of an element and is symbolized by 'Z'. It represents the number of protons found in the nucleus of an atom and is the defining trait of any element. The atomic number effectively determines the chemical characteristics of the atom, as it dictates the electron configuration and the way the element will interact in chemical reactions.

In the case of carbon-14, the atomic number is 6. This invariant attribute confirms that regardless of being an isotope, carbon-14 has the same chemical properties as other carbon atoms, primarily because its electron arrangement is identical. Understanding the atomic number is pivotal in identifying and differentiating between elements on the periodic table.

Neutrons in Nucleus

Neutrons are neutrally charged particles found within an atom's nucleus, accompanying protons, which have a positive charge. The number of neutrons can vary among atoms of the same element, resulting in different isotopes. Neutrons contribute to the mass of an atom but do not affect the chemical behavior in the same way that protons do.

For carbon-14, there are 8 neutrons in the nucleus. Carbon-14's nucleus composition defines its mass number, which is the sum of protons and neutrons, giving us a total of 14 (6 protons + 8 neutrons). This mass number is what distinguishes carbon-14 from carbon-12, which has 6 neutrons. It is the difference in neutron count among isotopes that can lead to variations in nuclear stability, decay patterns, and physical, though not chemical, properties.

Radiocarbon Dating

Radiocarbon dating is a scientific method used to determine the age of organic material by measuring the amount of carbon-14 it contains. Since carbon-14 is a radioactive isotope, it decays at a predictable rate over time. Living organisms constantly exchange carbon with their environment, keeping a consistent ratio of carbon-14 in their bodies. However, upon death, this exchange stops, and the carbon-14 present begins to decay.

The half-life of carbon-14, approximately 5,730 years, serves as the basis for estimating the time since the organism's death. By measuring how much carbon-14 remains in a sample and comparing it to the expected initial amount for a living organism, scientists can calculate its age. This technique is widely used in archaeology and geology to date ancient artifacts, fossils, and geological formations.