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


जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक