Answer:
The correct answer would be = t = 2.112 billion years
Explanation:
Given:
The number of crystal of uranium = 275 billion
The number of crystal of lead = 1925 billion
The half-life for 235U = 704 million years
Formula using :
N = N0e−λt
where,
no. of daughter atoms = N
at time t= 0, No. of parent atoms = N0.
Time = T
Half life = 0.693/λ
Decay constant = λ
Solution:
by putting value in the formula of the half-life
λ = 0.693/0.704
λ = 0.9844
Now, putting value in the formula for the age of granite.
275 = (275+1925)e^-0.9844 t
1/8= e^-0.9844 t
e^0.9844 t = 8
taking log
0.9844t = 2.07944
t = 2.112 billion years
The granite that contains zircon crystals with 275 billion 235U atoms and 1925 billion 207Pb atoms is 2112 million years old.
From the given information:
the total number of parent atoms is equal to the total number of ²³⁵U atoms
Now, from these 2200 billion atoms, 1925 billion of ²³⁵U atoms has changed to Pb²⁰⁷ atoms.
So when the number of half-life is: the parent atom is:
0 2200 billion
1 1100 billion
2 550 billion
3 275 billion
It implies that the parent atoms have passed through three half-life;
Thus, the age of the granite(parent atom) is calculated as:
age of granite = n × [tex]\mathbf{T_{1/2}}[/tex]
age of granite = 3 × 704 million years
age of granite = 2112 million years
Therefore, the age of granite is 2112 million years.
Learn more about half-life here:
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