Question

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?

• A. 100 days
• B. 1000 days
• C. 300 days
• D. 10 days

Answer 1

The correct option is B 1000 days

Say Permissible rate is $\vartheta$

then ${\vartheta }_2=100$

$\vartheta =kA$

$=k{A}_0{e}^{-kt}$

$kA_{0}e^{\frac{-0.693t}{t_{\frac{1}{2}}}}

$\vartheta ={\vartheta }_0{e}^{\frac{-0.693t}{t_{\frac{1}{2}}}}$

$\vartheta =10\vartheta e^{\frac{-0.693t}{t_{\frac{1}{2}}}}$

$l_n\left(10\right)=\frac{-0.693}{t_{\frac{1}{2}}}t$

$t=\frac{t_{\frac{1}{2}}\ast 2.303}{0.693}\ast 10$

$=1000$days