Use basic law of radioactive decay to show that radioactive nuclei follow an exponential decay law? Or State the law of radioactive decay .If No is the number of radioactive nuclei at some initial time t 0 ,find out the relation to determine the number N present at a subsequent time . Ans Radioactive decay Law:- The rate of decay of radioactive nuclei is directly proportional to the number of undecayed nuclei at that time . N λ Where .is the decay constant . Suppose initially the number of atoms in radioactive elements is N0 and the λ number of atoms after time t . According to Rutherford and Soddy law . N λ where disintegration constant . λ dt λ Integration loge N = t +C λ here c is a constant of integration . If N0 is initial number of radioactive nuclei ,then at t = 0,N= N0 ; so Loge N0 =0 + CC = loge N0 Substituting this equation in (1) ,we get Loge N loge N0 = t – λ Loge N / loge N0 = t λ N=N0e—λt Q:8 Define half life of radioactive substance .Establish its relation with the decay constant ? Or Define life of a radioactive sample .Using exponential decay law obtain the formula for the half of a – –life radioactive in terms of its disintegration constant/ Ans Half-life of a radioactive elements is define as the time in which number of radioactive nuclei becomes half of its initial value Expression for half time :-time radioactive decay equation is N = N0e—λt When t = T , N = Substituting and solving Or e-λt = 1/2 Taking log of both sides Or = loge 2 λT ****************************************
Use basic law of radioactive decay to show that radioactive nuclei follow an exponential decay law? Or State the law of radioactive decay .If No is the number of radioactive nuclei at some initial time t 0 ,find out the relation to determine the number N present at a subsequent time . Ans Radioactive decay Law:- The rate of decay of radioactive nuclei is directly proportional to the number of undecayed nuclei at that time . λ N Where λ .is the decay constant . Suppose initially the number of atoms in radioactive elements is N0 and the number of atoms after time t . According to Rutherford and Soddy law . λ N where λ disintegration constant . λ dt Integration loge N = λ t +C here c is a constant of integration . If N0 is initial number of radioactive nuclei ,then at t = 0,N= N0 ; so Loge N0 =0 + CC = loge N0 Substituting this equation in (1) ,we get Loge N – loge N0 = λ t Loge N / loge N0 = λ t N=N0e—λt Q:8 Define half life of radioactive substance .Establish its relation with the decay constant ? Or Define – life of a radioactive sample .Using exponential decay law obtain the formula for the half –life of a radioactive in terms of its disintegration constant/ Ans Half-life of a radioactive elements is define as the time in which number of radioactive nuclei becomes half of its initial value Expression for half time :-time radioactive decay equation is N = N0e—λt When t = T , N = Substituting and solving Or e-λt = 1/2 Taking log of both sides Or λT = loge 2 ****************************************