Chemistry Formulas for Nuclear Chemistry (Radioactivity) | Chemistry Notes Info - Your Chemistry Tutor provide notes for Classes, BSc, MSc, Chemistry Test

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 = 1.4x10-13cm

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 is curie (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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