A) A and B decay at the same rate always.
B) A and B decay at the same rate initially
C) A will decay at a faster rate than B.
D) B will decay at a faster rate than A.
Correct Answer: D
Solution :
[d] \[{{\left( {{T}_{1/2}} \right)}_{A}}={{\left( {{t}_{mean}} \right)}_{B}}\] \[\Rightarrow \,\,\,\,\,\,\frac{0.693}{{{\lambda }_{A}}}=\frac{1}{{{\lambda }_{B}}}\Rightarrow {{\lambda }_{A}}=0.693{{\lambda }_{B}}\] or \[{{\lambda }_{A}}<{{\lambda }_{B}}\] Also rate of decay \[=\lambda N\] Initially number of atoms (N) of both are equal but since \[{{\lambda }_{B}}>{{\lambda }_{A}},\] therefore B will decay at a faster rate than A
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