To explain the spontaneous decay of radioactive elements, Rutherford and Soddy put forward the theory of radioactive disintegration. According to this theory the quantity of a radioactive element which disappears in unit time is directly proportional to the amount (atoms) of radioactive substance present at that time.
Based on the above theory, the following equation is derived which confirms that all radioactive reactions follow I order
t = (2.303/λ) log (N0/N)
λ = decay constant
N0 = Number of radioactive atoms present initially
N = Number of radioactive atoms at time ‘t’