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QNEET-2013-Ph-1501: NEET 2013 Physics - Class 12 NEET-2013-Ph-1501 Solution: The half life of a radioactive isotope 'X' is 20 years. It…
The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be 80 years 100 years 40 years 60 years
Multiple Choice Options
- A 80 years
- B 100 years
- C 40 years
- D 60 years
Step-by-Step Verified Solution
Initial number of atoms of X is N 0
and Initial number of atoms of Y is 0
Number of atoms after time t, for X is N and for Y is N 0 - N
According to the question,
N N 0 _ N = 1 7
_ N N 0 = 1 8
As N N 0 = ( 1 2 ) n where n is the no. of half lives
_ ( 1 2 ) n = 1 8
_ n = 3
t = nT 1/2
= 3 _ 20 = 60 years
Hence, the age of rock is 60 years.