Question
Question: In a mean life of a radioactive sample :- (A) About 1/3 of substance disintegrate (B) Ab...
In a mean life of a radioactive sample :-
(A) About 1/3 of substance disintegrate
(B) About 2/3 of substance disintegrate
(C) About 90% of the substance disintegrate
(D) Almost all the substance disintegrates
Solution
Hint- here we can see that mean life is related with disintegration in all the option so we need to use formula for decay
Formula used
(N)=Noe−λt
Mean life(t)=T=N = \dfrac{{{N_o}}}{3}$$$$\dfrac{1}{\lambda }
Where is constant of proportionality or decay constant
Complete step by step solution
We know that expression for decay in terms of mean life
Radioactive nuclei(N)=Noe−λt
And Mean life(t)=T=\dfrac{1}{\lambda }$$$$\dfrac{1}{\lambda }
So putting the value of mean life in the decay formula
Radioactive nuclei (N)=Noe−λλ1
Here will cancel so we get
N=Noe−1
Or we can write N=eNo..........................(1)
Now we know that N−No
So in equation (1)
N=3No
Substance disintegration will be difference between original value(N) to obtained value(No)
ie: 32No
substituting the value of N in above equation
No−3No
Therefore substance disintegrated is 32No
So option (B) is correct
Note- radioactivity decay is a process which depends upon instability of the particular radioisotope. The decay process and observed half life dependence of radioactivity can be predicted by assuming that individual nuclear decay is a purely random event.