##
**Chemistry Formulas for Nuclear
Chemistry (Radioactivity)**

Empirical
relationship between size of nucleus and its mass number is

R = R_{0}A^{1/3}

Where,

R = radius of nucleus,

A = mass number,

R_{0} = contestant = 1.4x10^{-13}cm

###
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

Where,

N_{0} = No. of atoms
originally present,

N = No. of atoms present after time
t

###
Half Life Time (t_{1/2})

t_{1/2} = 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 (T_{1/2})

Where,

K = decay constant

T = Average Life Time

T_{1/2 }= 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 Ra^{226}
= 3.7 x 10^{10}dps

Where,

dps = disintegrations per second

millicurie
(mc) = 3.7 x 10^{7}dps

microcurie
(µc) = 3.7 x 10^{4}dps

Other
units of radioactivity are Rutherford (rd) and Becquerel (Bq).

####
Rutherford
(rd)

1rd = 10^{6}dps

####
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,

N_{A}/N_{B}
= K_{B}/K_{A} = T_{A}/T_{B}

Where,

K_{A} = radioactivity
constant for the process A---àB

K_{B} = radioactivity
constant for the process B---àC

T_{A} = average life period
of A

T_{B} = average life period
of B

Radioactive
Equilibrium in terms of half-life periods,

N_{A}/N_{B} = (T_{1/2})A/
(T_{1/2})B