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