Law of radioactive disintegration: According to Rutherford and Soddy law for radioactive decay is as follows, "At any point the rate of decay of radioactive atoms is proportional to the number of atoms present at that instant"
i.e. -dN/dt ∝ N =>dN/dt = -λn . It can be proved that N = N0e-λt
This equation can also be written in terms of mass i.e. M = M0e-λt
where N = Number of atoms remains undecayed after time t, N0 = Number of atoms present initially
(i.e. at t = 0), M = Mass of radioactive nuclei at time t, M0 = Mass of radioactive nuclei at time t = 0,
N0 - N = Number of disintegrated nucleus in time t
dN/dt= rate of decay, λ = Decay constant or disintegration constant or radioactivity constant or Rutherford Soddy's constant or the probability of decay per unit time of a nucleus.
Activity: It is defined as the rate of disintegration (or count rate) of the substance (or the number of atoms of any material decaying per second) i.e. A=-dN/dt = λN = λN0e-λt = A0e-λt
where A0 = Activity of t = 0, A = Activity after time t
Units of activity (Radioactivity): It's units are Becqueral (Bq), Curie (Ci) and Rutherford (Rd)
1 Becquerel = 1 disintegration/sec
1 Rutherford = 106 dis/sec,
1 Curie = 3.7 ´ 1011 dis/sec
Half life (T1/2): Time interval in which the mass of a radioactive substance or the number of it's atom reduces to half of it's initial value is called the half life of the substance.
i.e. if then
Hence from
![333_Radioactive disintegration3.png](https://www.expertsmind.com/../CMSImages/333_Radioactive disintegration3.png)
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Successive Disintegration and Radioactive Equilibrium: Suppose a radioactive element A disintegrates to form another radioactive element B which intern disintegrates to still another element C; such decays are called successive disintegration.
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![435_Radioactive disintegration1.png](https://www.expertsmind.com/../CMSImages/435_Radioactive disintegration1.png)
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Rate of disintegration of
(which is also the rate of formation of B)
Rate of disintegration of
Net rate of formation of B = Rate of disintegration of A - Rate of disintegration of B = λ1N1 - λ2N2
Equilibrium: In radioactive equilibrium, the rate of decay of any radioactive product is just equal to it's rate of production from the previous member.
i.e. ![1535_Radioactive disintegration6.png](https://www.expertsmind.com/CMSImages/1535_Radioactive%20disintegration6.png)
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