In this problem, we will use amounts of the isotopes that are proportional to the actual amounts. Trust me, this is mathematically sound. suppose you have a samle of potassium feldspar from a rhyolite and you measure the ratio of atoms of 40
AR to 40K of .024 to 1, or for every 10000 atoms of 40k you find 240 atoms of 4o
AR.
a. what is the ratio of atoms of radiogenic 40Ca to radiogenic 40
Ar.
b. what is the ratio of atoms radiogenic 40Ca to 40k
c. What is the daughter parent ratio ((40Ca+40
Ar)/40K)?
d. For every 10000 atoms of 40K in the sample today, how many atoms of radiogenic 40Ca plus 40
Ar are there now?
To answer these questions, let's break down the information provided.
Given:
- Ratio of atoms of 40Ar to 40K = 0.024 to 1 (or 240 atoms of 40Ar for every 10,000 atoms of 40K)
a. To find the ratio of atoms of radiogenic 40Ca to radiogenic 40Ar, we need to know the ratio of radiogenic 40Ca to 40K. However, this information is not provided in the given data. Therefore, we cannot find the exact ratio of atoms of radiogenic 40Ca to radiogenic 40Ar without additional information.
b. The ratio of atoms of radiogenic 40Ca to 40K can be calculated using a simple proportion. Since the ratio of atoms of 40Ar to 40K is 0.024 to 1, the ratio of atoms of radiogenic 40Ca to 40K can be calculated as follows:
(40Ca/40K) = (40Ar/40K) * (40Ca/40Ar)
Substituting the given ratio of atoms of 40Ar to 40K (0.024 to 1) and assuming the ratio of radiogenic 40Ca to 40Ar is "x," we can solve the proportion:
0.024/1 = (240/10000) * (x/240)
Simplifying the equation:
0.024 = 0.024x/10000
Cross-multiplying:
0.024 * 10000 = 0.024x
x = 240
Thus, the ratio of atoms of radiogenic 40Ca to 40K is also 240 to 1.
c. The daughter-parent ratio ((40Ca+40Ar)/40K) can be calculated by adding the number of atoms of 40Ca and 40Ar and dividing it by the number of atoms of 40K. Since the ratio of atoms of 40Ar to 40K is 0.024 to 1, we know that for every 10,000 atoms of 40K, there are 240 atoms of 40Ar.
Therefore, the daughter-parent ratio is:
((40Ca + 40Ar)/40K) = (240 + 10000)/(10000) = 10240/10000 = 1.024
The daughter-parent ratio is approximately 1.024.
d. Based on the given information, the number of atoms of radiogenic 40Ca plus 40Ar can be calculated by multiplying the number of atoms of 40K by the daughter-parent ratio (1.024).
For every 10,000 atoms of 40K, there are 1.024 * 10,000 = 10,240 atoms of radiogenic 40Ca plus 40Ar.
Therefore, for every 10,000 atoms of 40K in the sample today, there are approximately 10,240 atoms of radiogenic 40Ca plus 40Ar.