Question

the half life of radioactive sample against beta decay is 5500years.its initial activity is found to be 15 decays per minute per gram.in how much time would its activity reduce 10 decays per minute per gram.

Answer 1

use half life concept
t=0.693/K
where t is half life
and K is decay constant

so,
K=0.693/5500years
now use
dN/dt=-KN
dN/N=-K.dt
integrate and put limit
logNf-logNi=-Kt
logNi /Nf=Kt
now put Ni=15 decay /minute.gram
and Nf =10 decay/minute.gram
so,
log15/10=Kt
t= log1.5/K years
here you put K=0.693/5500years