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JEE Main 202229 JuneMorning Shift
Exam
JEE Main
Year
2022
Date
29 June
Shift
Morning Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2022 · 29 June · Morning Shift · Physics · Nuclear Physics

The activity of a radioactive material is 2 . 56 × 10 ^ - 3 Ci . If...

The activity of a radioactive material is 2.56×10−3Ci2 . 56 \times {10}^{- 3}Ci. If the half life of the material is 55 days, after how many days the activity will become 2×10−5Ci2 \times {10}^{- 5}Ci?

Options

  1. A3030 days
  2. B3535 days
  3. C4040 days
  4. D2525 days

Correct answer

B. 3535 days

Step-by-step solution

The activity of a radioactive sample at any time tt is given by,

A=A0(2)−tT12⇒2×10−5=2.56×10−3×2−t5⇒2t5=128⇒t5=7⇒t=35daysA = {A}_{0}{\left(2\right)}^{- \dfrac{t}{{T}_{\dfrac{1}{2}}}} ⇒ 2 \times {10}^{- 5} = 2 . 56 \times {10}^{- 3} \times {2}^{- \dfrac{t}{5}} ⇒ 2\dfrac{t}{5} = 128 ⇒ \dfrac{t}{5} = 7 ⇒ t = 35days

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