MCQ Solution: Chemical Kinetics
A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days. If the initial velocity is ten times the permissible value, after how many days will it be safe to enter the room?
1) 100 days
2) 1000 days
3) .300 days
4) 10 days
Solution
Say Permissible rate is $$\vartheta$$
then $$\vartheta _{2}=100$$
$$\vartheta =kA$$
$$=kA_{0}e^{-kt}$$
$$kA_{0}e^{\frac{-0.693t}{t_{\frac{1}{2}}}}
$$\vartheta =\vartheta _{0}e^{\frac{-0.693t}{t_{\frac{1}{2}}}}$$
$$\vartheta =10\vartheta e^{\frac{-0.693t}{t_{\frac{1}{2}}}}$$
$$l_{n}(10)=\frac{-0.693}{t_{\frac{1}{2}}}t$$
$$t=\frac{t_{\frac{1}{2}}*2.303}{0.693}*10$$
$$=1000$$days
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