JEE Main · 2007 · 29 Apr 2007 · Offline · Chemical Kinetics

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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?

(A)1000 days
(B)300 days
(C)10 days
(D)100 days✓ Correct

Answer: (D)

Solution

Activity is proportional to the number of radioactive atoms, which halves every half-life, so

\frac{N}{N _{0}} = (\frac{1}{2})^{n}

after

n

half-lives. To fall to one tenth,

(\frac{1}{2})^{n} = \frac{1}{10}

, so

n = \frac{l o g 10}{l o g 2} \approx 3.32

. Multiplying by the

30

-day half-life gives about

100

days before the room is safe to enter.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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