A G.M. counter is used to study the radioactive process of first-order. In the absence of radioactive…

A G.M. counter is used to study the radioactive process of first-order. In the absence of
radioactive substance $A$, it counts 3 disintegration per second (dps). When $A$ is placed in
the G.M. counter, it records 23 dps at the start and 13 dps after 10 minutes. It records $x$ dps
after next 10 minutes and $\mathrm{A}$ has half-life period y minutes. $\mathrm{x}$ and $\mathrm{y}$ are
  1. $8 \mathrm{dps}, 10 \mathrm{~min}$
  2. $5 \mathrm{dps}, 10 \mathrm{~min}$
  3. $5 \mathrm{dps}, 20 \mathrm{~min}$
  4. $5 \mathrm{dps}, 5 \mathrm{~min}$

Solution

There is error of 3 dps
$\therefore \mathrm{C}_{0}=20 \mathrm{dps}$
$C_{t}=10 \mathrm{dps}$
Thus, half-life $=10$ minutes
In next 10 minutes $C_{t}=5$ dps
$\therefore$ recorded value with error $=8 \mathrm{dps}$ ^

Asked in: JEE-TOPICTESTS-CHEMISTRY

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