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 :

• A. A and B is both decay at the same rate always
• B. A and B will decay at the same rate initially
• C. A will decay at a faster rate than B initially
• D. B will decay at a faster rate than A initially

Answer 1

The correct option is D B will decay at a faster rate than A initially

half life of $A=$ mean life of B_(1)

by intial atems of$A\left(\lambda A\right)$

= initial atams of $B\left({\lambda }_B\right)$

$=N_B$

from(1)

$\begin{array}{cc}{\left(t_{1/2}\right)}_A& ={\left(T_B\right)}_B\\ & \frac{0.693}{{\lambda }_A}=\frac{1}{{\lambda }_B}\\ \Rightarrow & {\lambda }_A=0.693{\lambda }_B\\ \Rightarrow & {\lambda }_A<{\lambda }_B\end{array}$

$\therefore B$ will decay faster

option D