Every radioactive isotope decays at a certain rate It is never known when a give

Question

Every radioactive isotope decays at a certain rate It is never known when a given nucleus will decay, but if many nuclei are gathered together, as a group they will decay at a measurable and consistent rate A radioactive half-life Is the time it will lake for half of the nuclei to decay Phosphorus 32 has a half life of 14 0 days. Starling with 6 00 g of^32P, how many grams will remain after 70 days? Express your answer numerically in grams. Carbon-14 has a half-life of 5736 years. In a plant fossil you find that the^14C has decayed to 1/6 0 of the original amount. How long ago was this plant alive? Express your answer numerically in years.

Explanation / Answer

A)
rate constant, K = 0.693/half life
= 0.693/14
= 0.0495 days-1

use:
[R] = [Ro]*e^*(-K*t)
=6*e^(-0.0495*70)
= 0.188 g
Answer: 0.188 g

B)
rate constant, K = 0.693/half life
= 0.693/5730
= 1.209*10^-4 Years-1

use:
[R] = [Ro]*e^*(-K*t)
[R] / [Ro] = e^*(-K*t)
1/16 = e^(-1.209*10^-4 * t)
t = 22933 years
Answer: 22933 years

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