BITSAT 2019 Slot 2 Solved Paper

Given, half life (T1∕2)=23.1 days
If N0 be the initial amount, then active nuclei
at t=15 days
N1=N0e−15λ ........(i)
Active nuclei at t=16 days
N2=N0e−16λ ........(ii)
Disintegration constant,
λ=

0.693

T 1 2

=

0.693

23.1

=0.03
∴% decay in 15th to 16th days
=

N1−N2

N1

×100 =

N0e−15λ−N0e−16λ

N0e−15λ

×100
=(1−e−λ)×100 =(1−e−0.03)×100
=(1−

1

e0.03

)×100 =(1−

1

1.03

)×100=2.9%