A granite contains zircon crystals with 275 billion 235 U atoms and 1925 billion
ID: 289748 • Letter: A
Question
A granite contains zircon crystals with 275 billion
235
U
atoms and 1925 billion
207
Pb
atoms. The half
-
life for
235
U
-
to
-
207
Pb
decay is 704 million years. How old is
the granite?
Hint:
In order to solve this problem, you have to calculate the to
tal
number of parent and daughter atoms (equaling the original number of parent
atoms when the rock formed) and then figure out how many half
-
lives have gone
by until the current number of parent atoms was reached (by repeatedly dividing
the original numbe
r by 2). The final step is to multiply this number of half
-
lives
with the years that correspond to one half
-
life
A granite contains zircon crystals with 275 billion
235
U
atoms and 1925 billion
207
Pb
atoms. The half
-
life for
235
U
-
to
-
207
Pb
decay is 704 million years. How old is
the granite?
Hint:
In order to solve this problem, you have to calculate the to
tal
number of parent and daughter atoms (equaling the original number of parent
atoms when the rock formed) and then figure out how many half
-
lives have gone
by until the current number of parent atoms was reached (by repeatedly dividing
the original numbe
r by 2). The final step is to multiply this number of half
-
lives
with the years that correspond to one half
-
life
A granite contains zircon crystals with 275 billion
235
U
atoms and 1925 billion
207
Pb
atoms. The half
-
life for
235
U
-
to
-
207
Pb
decay is 704 million years. How old is
the granite?
Hint:
In order to solve this problem, you have to calculate the to
tal
number of parent and daughter atoms (equaling the original number of parent
atoms when the rock formed) and then figure out how many half
-
lives have gone
by until the current number of parent atoms was reached (by repeatedly dividing
the original numbe
r by 2). The final step is to multiply this number of half
-
lives
with the years that correspond to one half
-
life
A granite contains zircon crystals with 275 billion
235
U
atoms and 1925 billion
207
Pb
atoms. The half
-
life for
235
U
-
to
-
207
Pb
decay is 704 million years. How old is
the granite?
Hint:
In order to solve this problem, you have to calculate the to
tal
number of parent and daughter atoms (equaling the original number of parent
atoms when the rock formed) and then figure out how many half
-
lives have gone
by until the current number of parent atoms was reached (by repeatedly dividing
the original numbe
r by 2). The final step is to multiply this number of half
-
lives
with the years that correspond to one half
-
life
A granite contains zircon crystals with 275 billion
235
U
atoms and 1925 billion
207
Pb
atoms. The half
-
life for
235
U
-
to
-
207
Pb
decay is 704 million years. How old is
the granite?
Hint:
In order to solve this problem, you have to calculate the to
tal
number of parent and daughter atoms (equaling the original number of parent
atoms when the rock formed) and then figure out how many half
-
lives have gone
by until the current number of parent atoms was reached (by repeatedly dividing
the original numbe
r by 2). The final step is to multiply this number of half
-
lives
with the years that correspond to one half
-
life
A granite contains zircon crystals with 275 billion
235
U
atoms and 1925 billion
207
Pb
atoms. The half
-
life for
235
U
-
to
-
207
Pb
decay is 704 million years. How old is
the granite?
Hint:
In order to solve this problem, you have to calculate the to
tal
number of parent and daughter atoms (equaling the original number of parent
atoms when the rock formed) and then figure out how many half
-
lives have gone
by until the current number of parent atoms was reached (by repeatedly dividing
the original numbe
r by 2). The final step is to multiply this number of half
-
lives
with the years that correspond to one half
-
life
Explanation / Answer
the number of crystal of uranium are 275 billion
The number of crystal of lead are 1925 billion
Now using formula N = N0et
here N = no. of daughter atoms.
N0 = No. of parent atoms at time t= 0. This is equal to the sum of parent and daughter atoms at time t.
T = time
= decay constant. Half life = 0.693/
thus = 0.693/0.704 = 0.9844
Thus using these values in the equation.
275 = (275+1925)e-0.9544 t
1/8= e-0.9544 t
e0.9544 t = 8
taking log both side
0.9544t = 2.07944
t = 2.112 billion years