Nuclear Physics And Radioactivity Question 65
Question: The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then [IIT 1999; UPSEAT 2003]
Options:
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
Show Answer
Answer:
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.
BETA
