Question

Radioactive isotopes in clastic sedimentary rocks always predict an age that is a) older than the sedimentary rock. b) younger than the sedimentary rock. c) correct for the sedimentary rock. The isotope of element X has 15 protons, 17 neutrons, and 15 electrons. The element has an atomic number of and a mass number of a) \(15 ; 32\) c) \(17 ; 47\) b) \(17 ; 15\) d) \(15 ; 30\) If radioactive decay began with 400,000 parent isotopes, how many would be left after three half-lives? a) 200,000 c) 50,000 b) 100,000 d) 25,000

Short answer

a) Older than sedimentary rock; Atomic: 15, Mass: 32; c) 50,000 isotopes.

Step-by-step solution

Understanding Radioactive Isotopes in Sedimentary Rocks

In clastic sedimentary rocks, radioactive isotopes used for dating often originate from older igneous or metamorphic rocks that get eroded and form sediments. Thus, when these sediments are dated, the ages reflect the time since the formation of the radioactive isotope in its original rock, which is always older than the sedimentary rock itself that formed later from these sediments.

Determining the Atomic and Mass Number

An element's atomic number is given by the number of protons, while the mass number is the sum of protons and neutrons. Here, element X has 15 protons and 15 electrons, making its atomic number 15. The mass number would be the sum of protons and neutrons, so it is \(15 + 17 = 32\). Thus, the atomic number is 15 and the mass number is 32.

Calculating Remaining Isotopes After Half-Lives

Radioactive decay reduces the number of parent isotopes by half every half-life. Starting with 400,000 isotopes, after one half-life, there would be \( \frac{400,000}{2} = 200,000\). After two half-lives, \( \frac{200,000}{2} = 100,000\). After three half-lives, \( \frac{100,000}{2} = 50,000\). Thus, 50,000 parent isotopes remain.

Key concepts

Radioactive Isotopes

Radioactive isotopes are unique versions of elements that have an unstable nucleus, causing them to lose particles over time. This process is known as radioactive decay.
In geology, radioactive isotopes are incredibly valuable as they serve as natural clocks that allow scientists to date rocks and minerals.

• These isotopes originate from processes that happened millions of years ago, usually from igneous or metamorphic rocks.
• The isotopes decay at a predictable rate, which is crucial for measuring geological timescales.

However, when dealing with clastic sedimentary rocks, the situation can be a bit misleading. Clastic sedimentary rocks are formed from fragments of older rocks, so when radioactive isotopes within these sediments are studied, they reflect the age of the original rock, not the sedimentary rock itself. Therefore, isotopic ages in such rocks are typically older than the rock formation itself.

Clastic Sedimentary Rocks

Clastic sedimentary rocks are formed from the accumulated fragments of pre-existing rocks. They are essentially made by compaction and lithification of sediments.

• These rocks are categorized based on their grain size - from clay-size particles in shales to large boulders in conglomerates.
• The formation involves transportation of material by wind, water, or ice, followed by deposition in a new location.

One key aspect of these rocks is their use in understanding past environmental conditions. Since radioactive isotopes in these rocks come from older rock fragments, they provide information about the history before the sediments were deposited. Understanding this helps geologists reconstruct ancient landscapes and timelines.

Atomic Number and Mass Number

Atoms are characterized by two fundamental numbers: atomic number and mass number.

• The atomic number is the number of protons in an atom, which defines the element's identity.
• The mass number is the total number of protons and neutrons in the nucleus.

For instance, in the element X, you have 15 protons and 15 electrons, so its atomic number is 15. When you add the 17 neutrons to this, the mass number becomes 32. These numbers not only help identify the element but also indicate its isotopic form. Knowing these characteristics can be fundamental in fields such as chemistry and geology, where understanding elemental composition is crucial.

Half-Life Calculation

The half-life of a radioactive isotope is the time it takes for half of the original amount of isotopes to decay. This concept is essential to understand how much of a radioactive substance remains over time.

• It's a constant time period that varies depending on the isotope, ranging from fractions of a second to billions of years.
• After each half-life, the quantity of the radioactive material reduces by half.

For example, if you start with 400,000 isotopes, after one half-life, you would have 200,000 remaining. After a second, you will have 100,000, and after three half-lives, only 50,000 isotopes would remain. Understanding half-life calculations is crucial not just for determining age in geology, but also in fields such as medicine and archaeology.