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NEET PHYSICSNUCLEIEasy

Question

For radioactive material, the half-life is 10 minutes. If initially, there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is:

A

20

B

10

C

30

D

15

Step-by-Step Solution

  1. Identify Given Values:
  • Half-life (T1/2T_{1/2}) = 10 minutes.
  • Initial number of nuclei (N0N_0) = 600.
  • Number of disintegrated nuclei = 450.
  1. Calculate Remaining Nuclei (NN):
  • N=N0disintegrated nucleiN = N_0 - \text{disintegrated nuclei}.
  • N=600450=150N = 600 - 450 = 150.
  1. Determine Decay Factor:
  • Ratio of remaining to initial nuclei: NN0=150600=14\frac{N}{N_0} = \frac{150}{600} = \frac{1}{4}.
  1. Relate to Half-Lives:
  • We know that 14=(12)2\frac{1}{4} = (\frac{1}{2})^2. This means 2 half-lives have passed (n=2n=2) .
  1. Calculate Time (tt):
  • t=n×T1/2t = n \times T_{1/2}.
  • t=2×10 minutes=20 minutest = 2 \times 10 \text{ minutes} = 20 \text{ minutes}.

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.

PHYSICSNUCLEIradioactivematerialhalflifeminutesinitially

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