Chemistry Formulas for Nuclear Chemistry (Radioactivity)

Chemistry Formulas for Nuclear Chemistry (Radioactivity)

Empirical relationship between size of nucleus and its mass number is
            R = R0A1/3
Where,                       
            R = radius of nucleus,
            A = mass number,
            R0 = contestant = 1.4×10-13cm

Rate of Decayof radioactive substance

Where,
            K = decay constant,
            N = No. of atoms,
            t = time of decay,
            dN = small fraction of N,
            dt = small fraction of t

Value of Decay Constant

            

Where,
            N0 = No. of atoms originally present,
            N = No. of atoms present after time t

Half Life Time (t1/2)

            t1/2 = 0.693/K
Where,
            K = decay constant

Average Life Time (T)

            Average life time (T) =Sum of the lives of the nuclei/ Total number of nuclei
            T = 1/K 
Also,
            Average life time (T) = 1.44 x Half-life (T1/2)
Where,
            K = decay constant
            T = Average Life Time
            T1/2 = Half Life

Specific Activity

            Specific Activity = Rate of decay/m
                                      = KN/m
                                      = K x Avogadro Number/ Atomic Mass in gram
Where,
            N = Number of Radioactive nuclei that undergoes disintegration

Units of Radioactivity

            Standard unit of radioactivity iscurie (c).
            1c = Activity of 1gram Ra226= 3.7 x 1010dps
Where,
            dps = disintegrations per second
millicurie (mc) = 3.7 x 107dps
microcurie (µc) = 3.7 x 104dps
Other units of radioactivity are Rutherford (rd) and Becquerel (Bq).

Rutherford (rd)

1rd = 106dps

Becquerel (Bq)

            Becquerel (Bq) is the SI unit of radioactivity.
                        1Bq = 1 disintegrations per second
                        1 Bq = 1 dps

Radioactive Equilibrium

            A —-à B —-à C
            At steady state,
                        NA/NB= KB/KA = TA/TB
Where,
            KA = radioactivity constant for the process A—àB
            KB = radioactivity constant for the process B—àC
            TA = average life period of A
            TB = average life period of B
Radioactive Equilibrium in terms of half-life periods,
            NA/NB = (T1/2)A/ (T1/2)B

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