Answer :
Answer:
Therefore, required equation is N = 100 x [tex]2^{- \frac{t}{5730 }[/tex]
Step-by-step explanation:
According to the question it is given that
Amount of carbon atom when animal was alive is [tex]N_0[/tex] = 100g
Half life of C-14 is 5730 years
Let 'N' be the amount of carbon atom present after 't' time
since the differential equation of decay process of radioactive atom is
[tex]\frac{dN}{dt} = \lambda N[/tex] where, λ is the decay constant
on solving this we get
[tex]N = N_0 e^{-\lambda t}[/tex]
on further solving and substituting [tex]\lambda = \frac{ln2}{T_{1/2}}[/tex] we get
[tex]N = N_0 2^{- \frac{t}{T_{1/2}} }[/tex]
on substituting the value of [tex]N_0[/tex] = 100g and [tex]T_{1/2}[/tex] = 5730 we get
N = 100 x [tex]2^{- \frac{t}{5730 }[/tex]