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JEE Main2007ChemistryChemical KineticsActual

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

Options

  1. A1000 days
  2. B300 days
  3. C10 days
  4. D100 days

Correct answer

D. 100 days

Step-by-step solution

Activity (- dN dt ) N N = N _ ( 1 2 )^ n N N _ = ( 1 2 )^ n 1 10 = ( 1 2 )^ n 10=2^ n 10= nlog 2 n = 1 0.301 =3.32 t = n t ₁₁₂=3.32 30=99.6 days Hence, (D) is correct.

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