Question

what fraction of the daughter material exist after 2 half - lives? objective 5: rewind your mind 1. how are minerals place into families/groups? 2. how are rocks classified? 3. give an example of a rock cycle process and how it impacts the appearance of the rock it forms 4. describe the mechanism for plate motion. 5. list and describe the movements of the 3 major plate boundary types. what landforms are created at each? 6. list and describe the motion (of the waves & the material they pass through) of the 3 types of seismic waves.

Explanation:

Step1: Recall half - life concept

The amount of daughter material after \(n\) half - lives for a radioactive decay is given by the formula related to the remaining parent material. The fraction of parent material remaining after \(n\) half - lives is \((\frac{1}{2})^n\). The fraction of daughter material \(f_d\) is \(1 - (\frac{1}{2})^n\).

Step2: Substitute \(n = 2\)

When \(n = 2\), we have \((\frac{1}{2})^2=\frac{1}{4}\). Then \(f_d=1-\frac{1}{4}=\frac{3}{4}\).

Minerals are placed into families/groups based on their chemical composition and crystal structure. For example, silicate minerals all contain silicon and oxygen and have similar structural characteristics.

Rocks are classified into three main types: igneous, sedimentary, and metamorphic. Igneous rocks form from the cooling and solidification of magma or lava. Sedimentary rocks form from the accumulation and compaction of sediments. Metamorphic rocks form from pre - existing rocks that are changed by heat, pressure, and chemical processes.

An example of a rock - cycle process is the formation of sedimentary rock from igneous rock. Weathering and erosion break down igneous rock into sediments. These sediments are then transported and deposited. Over time, through compaction and cementation, they form sedimentary rock. This process changes the appearance from a solid, often crystalline igneous rock to a layered sedimentary rock made of small particles.

Answer:

\(\frac{3}{4}\)

1.