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 Decay
of 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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