Two radioactive substance A and B have decay constants $$9$$λ and $$3$$λ respectively. At t $$=$$ $$0$$ , they have the same number of nuclei. The ratio of number of nuclei of A to these of B will be $$1e2$$ after a time interval of

Question

Two radioactive substance A and B have decay constants $$9$$λ and $$3$$λ respectively. At  t $$=$$ $$0$$ , they have the  same number of nuclei. The ratio of number of nuclei of A to these of B will be  $$1e2$$ after a time interval of

Infinity Learn · Accepted Answer

Decay Law, N $$=$$ $$Noe-$$λt Case $$1$$ : $$N1=Noe$$−λ$$1t=Noe$$−$$9$$λt Case $$2$$ : $$N2=Noe$$−λ$$2t=Noe$$−$$3$$λt Dividing them,  $$N1N2=Noe-9$$λtNoe−$$3$$λ$$t=e$$−$$6$$λt But $$N1N2=1e2$$ ⇒  e−$$6$$λ$$t=e$$−$$2$$ ⇒$$6$$λ$$t=+2$$ ⇒$$t=26$$λ$$=13$$λ

Two radioactive substance A and B have decay constants $9 λ$ and $3 λ$ respectively. At t = 0 , they have the same number of nuclei. The ratio of number of nuclei of A to these of B will be $\frac{1}{e^{2}}$ after a time interval of

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Two radioactive substance A and B have decay constants 9λ and 3λ respectively. At t = 0 , they have the same number of nuclei. The ratio of number of nuclei of A to these of B will be 1e2 after a time interval of

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Two radioactive substance A and B have decay constants $9 λ$ and $3 λ$ respectively. At t = 0 , they have the same number of nuclei. The ratio of number of nuclei of A to these of B will be $\frac{1}{e^{2}}$ after a time interval of