Answer :
The granite sample is 2.6 billion years old.
What materials make up granite?
Granite is a pale-colored plutonic rock that is primarily found in mountainous regions of the continental crust. It is made up of sodium feldspar, potassium feldspar, and coarse quartz grains (10–50%). Upwards of 80% of the rock is composed of these minerals.
Briefing :
Given ,As we know that the radioactive decays follow the first order kinetics.
First we have to calculate the rate constant.
Formula used : [tex]t\frac{1}{2}[/tex] = [tex]\frac{0.693}{k}[/tex]
[tex]1.3 billion years[/tex] = [tex]\frac{0.693}{k}[/tex]
[tex]k = 0.533 ( billion years )^{-1}[/tex]
Now we have to calculate the age of the sample of granite.
The expression for rate law for first order kinetics is given by :
[tex]k = \frac{2.303}{t}[/tex] [tex]log \frac{a}{a-x}[/tex]
where,
k = rate constant = 0.533
t = time taken for decay process = ?
a = initial amount of the reactant = 100 g
a - x = amount left after decay process = 100 - 75 = 25 g
Putting values in above equation, we get the age of the sample of granite.
[tex]0.533 = \frac{2.303}{t} log \frac{100}{25}[/tex]
t = 2.6 billion years
Therefore, the age of the sample of granite is, 2.6 billion years
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