how to calculate half life decay

 we can calculate the half-life of any  atom  by using the relation.

 

Where lambda is the decay constant

 Half life is the time taken for the half the mass or energy of a radioactive sample to decay by half.

 Let us give an example  to see how to calculate the halflife of  a given sample or atoms.

Examples

1.     An element source has  a decay constant of 1.36×10^-11s^-1, calculate the halflife of the  element.

Given that
 

Therefore after  every 5.09×10¹⁰ seconds half of the original mass of this sample will disappear ,

 we can find this half life in  minute, hours   anddays months and years

 there fore

the halflife is equal to  843333333.333 minutes

14055555.555 hours , meaning this hours 50 % of the original mass will disappear.

Which is also equal to 585648.148 days

 And also equal to 1614 years

  how do we do that ?

 To convert  the half life from second to year , we divide the answer by  60×60 ×24 ×365

 

2.     Calculate  the half life of a radioisotopes  which has a decay constant of 0.000456 per day

Using

 

 

3.     The original quantity ofa radio-isotopenis given as 100gram if the quantity remaining after 6 days is 75 grams , calculate the (a) decay constant (b) half life of radio-iostopes

Solution     

Using the   formula

Where t =6 days, N ₀=100grams and N=75grams , substituting the above values into the equation below , we have