part 1:
at any time, number of nuclei is N and initial number of nuclei
is N0.
then dN/dt=-k*N
where k is a constant.
(-ve sign is because of the fact that with increasing time,
number of nuclei decreases)
hence dN/N=-k*dt
integrating both sides,
ln(N)=-k*t+c
at t=0, N=N0
==>ln(N0)=c
then ln(N)=-k*t+ln(N0)
==>ln(N/N0)=-k*t
==>N/N0=exp(-k*t)
==>N=N0*exp(-k*t)
part c:
mass of isotope produced=0.45 kg
molar mass of 90Sr=90 grams
number of moles produced=total mass/molar mass=0.45/(0.09)=
=5 moles
=5*6.022*10^23 nuclei
number of nuclei per m^2 of area=total number of nuclei/total
area
=5*6.022*10^23/(110*10^6 m^2)
=2.7373*10^16
half life=29 years
then decay constant=ln(2)/half life=ln(2)/(29*365*24*3600
seconds)
=7.5792*10^(-10) s^(-1)
activity=number of nuclei*decay constant
==>9.2*10^4=number of nuclei*7.5792*10^(-10)
==>number of nuclei=1.214*10^14
then area=number of nuclei/nuclei per m^2
=1.214*10^14/(2.7373*10^16)
=0.004435 m^2
