AP EAPCET 18 May 2024 Shift 1 Solved Paper

Given:
Initial amount of A1=40g
Initial amount of A2=160g
Half-life of A1,TA1=20s
Half-life of A2,TA2=10s
To determine when the amounts of A1 and A2 will be equal, we use the decay formula:
N=N0(‌

1

2

)t∕T
For A1, the remaining amount is:
NA1=40(‌

1

2

)t∕20
For A2, the remaining amount is:
NA2=160(‌

1

2

)t∕10
To find the time when these amounts are equal, set NA1=NA2 :
40(‌

1

2

)t∕20‌=160(‌

1

2

)t∕10
2t∕10‌=4⋅2t∕20⇒2‌

t

10

−‌

t

20

=4
2t∕20‌=22⇒‌

t

20

=2
t‌=40s
Therefore, the amounts of A1 and A2 in the mixture will become equal after 40 seconds.