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The half-life period of 234 U is 2.5 × 10 5 years. In how much time is the quantity of the isotope reduced to 25% of the original amount-

Options

  1. A5 × 10 5 years
  2. B4 × 10 5 years
  3. C6 × 10 5 years
  4. D3 × 10 5 years

Correct answer

A. 5 × 10 5 years

Step-by-step solution

Initial amount of this isotope N 0 = 100 Final amount of the isotope N = 25 We know that N = ( 1 2 ) n N 0 So, 25 = ( 1 2 ) n × 100 or 25 100 = ( 1 2 ) n or 1 4 = ( 1 2 ) n o r ( 1 2 ) 2 = ( 1 2 ) n or n = 2 Time taken T = n × t 1 2 = 2 × 2.5 × 10 5 = 5 × 10 5 years

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