In: Advanced Math
Question 3 A A A Carbon-14 (C14) decays by a nuclear process to form carbon-12 (C12). The rate of decay of C14 is directly proportional to the quantity of C14 present. The half-life of C14 (time taken for the mass of C14 to halve, eg 1.0kg to 0.5kg) is 5730 years. If you start with a 883 gram block of pure C14, what mass of C14 remains after 2922 years? Provide your answer to TWO decimal places, using the normal convention. Pad with zeros if necessary. Mass of C14 at 2922 years (g) =
given data:
Initial weight of C14 = 833 gm
half life = 5730 years
to find is the weight remaining after 2922 years
since decay rate is proportional to present quantity, then we can write
where 'k' is the proportionality constant. -ve sign indicates that rate is negative as mass is decreasing. Further solving the differentiall equation based no initial condition:
integrating the above equation from t = 0 to t, we get:
putting W = 833 at t = 0, we get:
so,
now at t = 5730, w(5730) = 833/2 gm;
hence,
now at t = 2922, we find w(t):
hence remaining weight if 584.95 gram.
hope the solution is clear and sound. Please ask question if there is any doubt, thank you.