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The half-life for the radioactive decay of C?14 is 5730 years. How long will it

ID: 808166 • Letter: T

Question

The half-life for the radioactive decay of C?14 is 5730 years. How long will it take for 20% of the C?14 atoms in a sample of C?14 to decay? If a sample of C?14 initially contains 1.5mmol of C?14, how many millimoles will be left after 2245 years?

The density of an unknown metal is 8.94g/cm3 and its atomic radius is 0.126nm . It has a face-centered cubic lattice. Find the atomic weight of this metal.

If a temperature increase from 20.0?C to 33.0?C triples the rate constant for a reaction, what is the value of the activation barrier for the reaction?

Please explain how you reached your answer. Thank you so much!

Explanation / Answer

One form of the first order rate equation is-

ln(Ao/A) = kt

where Ao = the initial concentration and A = the concentration after time t. k = the rate constant.

If t = the half life, then Ao/A = 2 and ln(2) = 0.693

0.693 = k * 5730 yr

k = 1.210x10^-4 yr^-1

If 30% decays, 70% is left

ln(100/70) = 1.210x10^-4 * t

t = 2949 year

ln(1.7 mmol/X mmol) = 1.210x10^-4 x 2285

ln(1.7/X) = 0.2764

1.7/X = 1.318

X = 1.7/1.318 = 1.289 mmol

1.3 mmol left after 2285 years