Verified Solution • 2025–26 Session moderate

QJEEM07Ch102e: JEE Main 2007 Chemistry - Class 12 JEEM07Ch102e Solution: A radioactive element gets spilled over the floor of a room.…

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?

Multiple Choice Options

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

Step-by-Step Verified Solution

Suppose activity of safe working =A=A

Given A0=10A{A_0} = 10A

λ=0.693t1/2=0.69330\lambda = {{0.693} \over {{t_{1/2}}}} = {{0.693} \over {30}}

t1/2=2.303λlog⁡A0A

=2.3030.693/30log⁡10AA= {{2.303} \over {0.693/30}}\log {{10A} \over A}

=2.303×300.693×log⁡10= {{2.303 \times 30} \over {0.693}} \times \log 10

=100= 100 days.

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