Question 548: Atoms & Nuclei

Question

The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was 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,
$${N \over {{N_0} - N}}$$ = $${1 \over 15}$$
$$ \Rightarrow $$ $${N \over {{N_0}}} = {1 \over 16}$$
As $${N \over {{N_0}}} = {\left( {{1 \over 2}} ight)^n}$$ where n is the no. of half lives
$$ 	herefore $$ $${\left( {{1 \over 2}} ight)^n} = {1 \over 16}$$
$$ \Rightarrow $$ n = 4
t = nT
1/2
= 4 ÃÂ 50 = 200 years
Hence, the age of rock is 200 years.

Answer

150 years

Answer

200 years

Answer

250 years

Answer

100 years

Atoms & Nuclei

The half life of a radioactive isotope X is 50 years. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1 : 15 in a sample of a given rock. The age of the rock was estimated to be

Choose the correct answer: