**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 = 1.4×10^{-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

### Value of Decay Constant

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/KWhere,

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}dpsWhere,

dps = disintegrations per second

millicurie (mc) = 3.7 x 10

^{7}dpsmicrocurie (µc) = 3.7 x 10

^{4}dpsOther 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 BRadioactive Equilibrium in terms of half-life periods,

N

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