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(a) Define the terms (i) half-life (T_(1//2) ) and (ii) average life (tau). Find out their relationships with the decay constant ( lambda). (b) A radioactive nucleus has a decay constant, lambda = 0.3465 (day)""^(-1). How long would it take the nucleus to decay to 75% of its initial amount? |
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Answer» Solution :(a) Definition : (i) Half life : Time taken by a RADIOACTIVE nuclei to reduce to half of the initial number of radionuclei. (ii) Average life : Ratio of TOTAL life time of all radioactive nuclei to the total number of nuclei in the sample. Relation between half life and decay constant : `T_(1//2) = (0.693)/( lambda)` Relation between average life and decay constant `tau = (1)/(lambda)`. (b) `N= N_(0) e^(- lambda t)` `(3)/(4) N_(0) = N_(0) e^(-(0.3465) t) ""(because N= 75% "of" N_(0) )` `N= (3)/(4) N_(0)` `e^((0.3465)t) = (4)/(3)` `0.3465 XX t= log_(e) (4//3)` `=2.303 [ log4-log3]`. `=2.303 [0.6020-0.4771]` `=2.303 xx 0.1249` `t=(2.303 xx 0.1249) /( 0.3465)` `THEREFORE t=0.83` days or 19.92 HOURS |
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