Question
A Geigger Muller counter is used to study the radioactive process. In the absence of radioactive substance $$A,$$ it counts 3 disintegration per second $$(dps).$$ At the start in the presence of $$A,$$ it records $$23\,dps;$$ and after $$10\,\min \,13\,dps,$$
(i) What does it count after $$20\,\min $$
(ii) What is the half life of $$A?$$
A.
$$8\,dps,10\,\min $$
B.
$$5\,dps,10\,\min $$
C.
$$5\,dps,20\,\min $$
D.
$$5\,dps,5\,\min $$
Answer :
$$8\,dps,10\,\min $$
Solution :
In the absence of $$A,3\,dps$$ is zero error, hence
Initial count $$ = 23 - 3 = 20\,dps$$
After $$10\,\min = 13 - 3 = 10\,dps$$
After $$20\,\min = 5\,dps$$
( recorded $$ = 5 + 3 = 8\,dps$$ )
( $$50\% $$ fall in $$10\,\min ,{T_{50}} = 10\,\min $$ )