Question 583: Atoms & Nuclei

Question

A  mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after

Accepted Answer

Let, the amount of the two in the mixture
will become equal after t years.
The amount of A
1
, which remains after t years
N
1
= $${{{N_{01}}} \over {{{\left( 2 \right)}^{t/20}}}}$$
The amount of A
2
, which remains, after t years
N
2
= $${{{N_{02}}} \over {{{\left( 2 \right)}^{t/10}}}}$$
According to the question
N
1
= N
2
$$ \Rightarrow $$ $${{40} \over {{{\left( 2 \right)}^{t/20}}}} = {{160} \over {{{\left( 2 \right)}^{t/10}}}}$$
$$ \Rightarrow $$ $${{{\left( 2 \right)}^{t/20}}}$$ = $${{{\left( 2 \right)}^{\left( {{t \over {10}} - 2} \right)}}}$$
$$ \Rightarrow $$ $${{t \over {20}} = \left( {{t \over {10}} - 2} \right)}$$
$$ \Rightarrow $$ t = 40 s

Answer

60 s

Answer

80 s

Answer

20 s

Answer

40 s

Atoms & Nuclei

A mixture consists of two radioactive materials A1 and A2 with half lives of 20 s and 10 s respectively. Initially the mixture has 40 g of A1 and 160 g of A2. The amount of the two in the mixture will become equal after

Choose the correct answer: