Define the term 'decay constant' of a radioactive sample. The of disintergration of a given radioactive nucleus is 10000 disintegrations/s and 5,000 disintegration/s after 20 hr. and 30 hr. respectively from start. Calculate the half life and initial number of nuclei at t = 0.

Explanation

Radioactive constant of a fsubtance may be difined as the reciprocal of the time, after which the number of atoms of a radioactive sbstance decreases to 0.368 (or 36.8%) of their number of atoms preent initially.
`R=R_(0)e^(-lamdat)`
`10000=R_(0)e^(-lamda(20)" ...(1)")`
`5000=R_(0)e^(-lamda(30)" ...(2)")`
dividing equation no. (1) by (2)
`2=e^(-lamda(-10))`
`rArr" "lamda=0.0693hr^(-1)`
`"Half life T"_(1//2)=(0.693)/lamda=(0.693)/(0.0693)=10" years"`
`R=lamdaN_(0^(e^(-lamdat)))`
`N_(0)=R/(lamdae^(-lamdat))`
`N_(0)=(10,000)/(0.0693xxe^(-0.0693xx20))`
`N_(0)=577200.57=577200" atoms".`