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NEET PHYSICSNUCLEIMedium

Question

A human body required the 0.01 Curie0.01\text{ Curie} activity of a radioactive substance after 24 hours24\text{ hours}. The half-life of the radioactive substance is 6 hours6\text{ hours}. The maximum activity of the radioactive substance that can be injected will be:

A

0.08

B

0.04

C

0.16

D

0.32

Step-by-Step Solution

Radioactive decay follows first-order kinetics . The activity (AA) of a sample after a period of time is related to its initial activity (A0A_0) by the number of half-lives (nn) that have passed, using the formula A=A0/2nA = A_0 / 2^n .

Given the following data:

  • Final activity required (AA) = 0.01 Curie0.01\text{ Curie}
  • Total time elapsed (tt) = 24 hours24\text{ hours}
  • Half-life (T1/2T_{1/2}) = 6 hours6\text{ hours}
  1. Calculate the number of half-lives (nn): n=tT1/2=246=4n = \frac{t}{T_{1/2}} = \frac{24}{6} = 4 half-lives.

  2. Calculate the initial activity (A0A_0): 0.01=A0240.01 = \frac{A_0}{2^4} 0.01=A0160.01 = \frac{A_0}{16} A0=0.01×16=0.16 CurieA_0 = 0.01 \times 16 = 0.16\text{ Curie}.

Therefore, the initial activity to be injected is 0.16 Curie0.16\text{ Curie}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from NUCLEI. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSNUCLEIrequiredactivityradioactivesubstancehalflife

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