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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 velocity is ten times the permissible value, after how many days will it be safe to enter the room?

  • Option 1)

    100 days

  • Option 2)

    1000 days

  • Option 3)

    300 days

  • Option 4)

    10 days.

 

Answers (1)

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As we learned

Number of nuclei in terms of half life -

N=\frac{N_{0}}{2^{t/t_{1/2}}}

- wherein

Very useful to determine number of nuclei in terms of half life

 

 Given \: I_{0}=10\, I\\* from\: I=I_{0}\: e^{-\lambda t}\\* I = 10 I\: e^{-\lambda t}\\* e^{-\lambda t}= \frac{1}{10}

t= \left ( \frac{\ln 10}{\ln 2} \right )\cdot \lambda \\* t=3.32\times 30\\* = 99.6\cong 100\: days

Ans is 1


Option 1)

100 days

Option 2)

1000 days

Option 3)

300 days

Option 4)

10 days.

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Plabita

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