Question

Carbon (Z = 6) with mass number 11 decays to boron (Z = 5). (a) Is it a β+ -decay or a β− -decay? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90 % carbon - 11 and 10% boron - 11 (by the number of atoms ) converts itself into a mixture of 10% carbon - 11 and 90 % boron - 11 ?

Solution

(a)P→n+e−+v Hence it is aβ−decay (b)Let the total no. of atoms be100 N1 Carbon              Boron Initially              90 N            10N0 Fimlly             10N0               90 N0 Now,10N0=90 N0 e−λt ⇒19=e−0.69820.8×t ∵t12=20.3min ⇒ln19=−0.69320.3t ⇒t=2.1972×20.30.693 = 64.36=64min

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