Atoms And Nuclei Question 395
Question: The half-life of a radioactive element A is the same as the mean-life of another radioactive element B. Initially both substances have the same number of atoms, then:
Options:
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.
Show Answer
Answer:
Correct Answer: D
Solution:
- $ {{( {T _{1/2}} )} _{A}}={{( t _{mean} )} _{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
