Question 580: Atoms & Nuclei

Question

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

Accepted Answer

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,
$${N \over {{N_0} - N}}$$ = $${1 \over 7}$$
$$ \Rightarrow $$ $${N \over {{N_0}}} = {1 \over 8}$$
As $${N \over {{N_0}}} = {\left( {{1 \over 2}} ight)^n}$$ where n is the no. of half lives
$$ 	herefore $$ $${\left( {{1 \over 2}} ight)^n} = {1 \over 8}$$
$$ \Rightarrow $$ n = 3
t = nT
1/2
= 3 ÃÂ 20 = 60 years
Hence, the age of rock is 60 years.

Answer

80 years

Answer

100 years

Answer

40 years

Answer

60 years

Atoms & Nuclei

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

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