The carbon in living organisms contains about 1.3 atoms of ^14 C for every 10^12 atoms of all k

Step 1: We are given that there are 1.3 atoms of ${ }^{14} mathrm{C}$ for every $10^{12}$ atoms

The carbon in living organisms contains about 1.3 atoms of ...

The carbon in living organisms contains about $1.3$ atoms of ${ }^{14} \mathrm{C}$ for every $10^{12}$ atoms of all kinds of carbon, and the half-life of ${ }^{14} \mathrm{C}$ is 5730 years. (a) How many decays would one expect per minute from $7 \mathrm{~g}$ of carbon taken from a living tree? (b) If $7 \mathrm{~g}$ of carbon is extracted from a wooden beam of a prehistoric dwelling and if they undergo 10 decays per minute, about how old is the dwelling?

Key Concepts

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. Over time, the number of unstable nuclei decreases exponentially as they transform into more stable configurations. This fundamental process is used to predict how substances diminish over time, forming the basis for many dating techniques and scientific analyses.

Half-Life

The half-life of a radioactive isotope is the time required for half of its nuclei to decay. It is a key characteristic of a radioactive substance, helping to determine the rate at which it decays. Knowing the half-life allows scientists to calculate the age of a sample by comparing its current amount to its original quantity.

Exponential Decay Equation

The exponential decay equation mathematically describes how the quantity of a radioactive substance decreases over time. This equation incorporates the decay constant, which is directly related to the half-life, and is central to predicting the remaining number of radioactive atoms after a given time period.

Isotopic Abundance

Isotopic abundance refers to the relative proportion of a specific isotope compared to all isotopes of an element present in a sample. This concept is important in radiometric dating because the initial abundance of the radioactive isotope is used as a reference point for determining the extent of decay over time.

Activity Measurement

Activity is the rate at which radioactive decays occur, usually measured in decays per minute or per second. This measurement reflects the remaining amount of a radioactive isotope in a sample and, when compared against a known standard, can be used to infer the age of the sample.

Radiometric Dating

Radiometric dating uses the known decay rate of radioactive isotopes to determine the age of materials. By measuring the current activity of a radioactive isotope and comparing it to its original level, scientists can calculate how much time has elapsed since the material was formed. This technique is widely applied in fields such as archaeology, geology, and paleontology.

Please give Ace some feedback