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90% of the radioactive sample is left over after a time interval t. The percentage of initial sample that will disintegrate in an interval 2t is

Asked by sudheerkapoor67 15th October 2017, 9:13 PM
Answered by Expert
Answer:
Radioactivity relation is given by 
 
N space equals space N subscript 0 e x p left parenthesis negative lambda t right parenthesis

H e n c e space N over N subscript 0 space equals space 0.9 space equals space e x p left parenthesis negative lambda t right parenthesis
ln left parenthesis 0.9 right parenthesis space equals space minus lambda t space semicolon space h e n c e space lambda space equals space fraction numerator negative ln left parenthesis 0.9 right parenthesis over denominator t end fraction

N o w space f o r space 2 t space i n t e r v a l comma space p e r c e n t a g e space o f space i n i t i a l space s a m p l e space t h a t space w i l l space d i sin t e g r a t e space i s
space N over N subscript 0 space equals space e x p left parenthesis negative lambda 2 t right parenthesis space space equals space e x p open parentheses fraction numerator ln left parenthesis 0.9 right parenthesis over denominator t end fraction space 2 t close parentheses space equals space e x p left parenthesis 2 ln left parenthesis 0.9 right parenthesis right parenthesis space equals space 0.81

H e n c e space t h e space a n s w e r space i s space 81 percent sign
Answered by Expert 16th October 2017, 1:11 PM
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