Two different radioactive elements with half-lives ' T ₁ ' and ' T ₂ ' have undecayed atoms ' N ₁ ^ and ^ N ₂ ^ respectively, present at a given instant. The ratio of their activities at this instant is

Step-by-step solution

Activity, R (= dN dt )= N Decay constant = _ e 2 ~T Activity R= ( _ e 2 ) N T R ₁= ( _ e 2 ) N ₁ ~T ₁ , R ₂= ( _ e 2 ) N ₂ ~T ₂ For two elements R₁ R₂ = N₁ T₁ T₂ N₂ = ( N₁ N₂ )= ( T₂ T₁ )