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NEET PHYSICSNUCLEIEasy

Question

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

A

2/3

B

2/3√2

C

1/2

D

1/2√2

Step-by-Step Solution

  1. Identify the Concept: Radioactive decay follows first-order kinetics . The activity (AA) remaining after time tt is related to the initial activity (A0A_0) by the formula A=A0(12)nA = A_0 (\frac{1}{2})^n, where nn is the number of half-lives elapsed .
  2. Calculate Number of Half-lives (nn):
  • Given Half-life (T1/2T_{1/2}) = 100 hours.
  • Given Time elapsed (tt) = 150 hours.
  • n=tT1/2=150100=1.5=32n = \frac{t}{T_{1/2}} = \frac{150}{100} = 1.5 = \frac{3}{2}.
  1. Calculate Fraction of Activity:
  • Fraction remaining = AA0=(12)n\frac{A}{A_0} = (\frac{1}{2})^{n}.
  • AA0=(12)3/2=121×20.5=122\frac{A}{A_0} = (\frac{1}{2})^{3/2} = \frac{1}{2^1 \times 2^{0.5}} = \frac{1}{2\sqrt{2}}.

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.

PHYSICSNUCLEIhalfliferadioactivenuclidefractionoriginal

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