JEE MainChemistryToughPhysical Chemistry

A radioactive element gets spilled over the floor of a room. Its
half-life period is 30days. If the initial activity is ten times the
permissible value, after how many days will it be safe to enter the
room

Show answer and solution

Let A be the activity for safe working
Given

A_{0} = 10A

Ao \times No\ and\ A \times N

t = \frac{2.303}{\lambda}\log\frac{N_{0}}{N} = \frac{2.303}{\lambda}\log\frac{A_{0}}{A}

= \frac{\frac{2.303}{0.693}}{30}\log\frac{10A}{A} = \frac{2.303 \times 30}{0.693}\log 10 = \frac{2.303 \times 30}{0.693} = 99.69days \approx 100\ days\

Source: Grass-G / CH-28 Chemistry Paper FST 16 Jan.docx

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