Average & half life

source : www.nde-ed.org

**Average Life Period & half life period-**

## Half Life Period-

### “It is equal to the time required to disintegrate half of the quantity of the radioactive element taken”.

or

### “Half life period is the time during which half of the quantity of a sample of radioactive element disintegrates.”

*Half life is represented by t _{1/2}. The value of t_{1/2 } does not depend upon temperature, pressure, catalyst and mass of radioactive substance taken etc.*

*t _{1/2 }is a measure of radioactivity and stability of radioactive element. Greater is the value of t_{1/2}, greater is the stability of the radioactive element & smaller is its radioactivity.*

*Ex.- Half life of Ra ^{226} is 1580 years. This shows that after 1580 years, the mass of radium is half of the mass taken.*

*After 2×1580 (=3160 year) the quantity of Ra ^{226} left will be ¼ ( one fourth) of the mass taken.*

*Suppose initial mass or no. of atoms of a radioactive element is No. its half life period is t _{1/2}*

*After one t _{1/2}atoms left = No/2*

*Atoms left after two half lives = No/4=No/2 ^{2}*

*After three half lives atoms left= No/8 = No/2 ^{3}*

* Atoms left after ‘n’ half lives= No/2 ^{n}*

*The mass or no. of atoms left after ‘n’ half lives is ‘N’*

*N= No(1/2)*^{n}

^{n}

*T=n×t*_{1/2}

_{1/2}

## Relation between disintegration constant and half life-

* Radioactive disintegration is 1 ^{st} order reaction . for First order Reaction,*

*K = ( 2.303 / t ) log a /(a- x) *

*If t= t _{1/2 }, & x = a/2 then,*

*K = ( 2.303 / t _{1/2} ) log a /(a- a/2) *

*K = ( 2.303 / t _{1/2} ) log 2*

*because , log2 = 0.3010*

*K = ( 2.303 x 0.3010 / t _{1/2} ) *

*K = 0.693 / t*_{1/2}

_{1/2}

**Average Life Period-**

**Average Life Period-**

* “Reciprocal of t _{1/2} of a radioactive element is called its average life period.”*

*It is represented by τ (Tau)*

*τ =1/K*

*K= 0.693 /t _{1/2}*

K = *t _{1/2} / 0.693*

*Average life (τ) =1.44×t*_{1/2}

_{1/2}