« previous 10 of 20 next » ± Radioactive Half-lives Part A Every radioactive iso

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« previous 10 of 20 next » ± Radioactive Half-lives Part A 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 take for half of the nuclei to decay Phosphorus-32 has a half-life of 14.0 days. Starting with 8.00 g of 32P, how many grams will remain after 98.0 days? Express your answer numerically in grams Hints 28 Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B Carbon-14 has a half-ife of 5730 years. In a plant fossil, you find that the 14C has decayed to 1/4.00 of the original amount. How long ago was this plant alive? Express your answer numerically in years Hints years Submit My Answers Give Up

Explanation / Answer

A)
Given:
Half life = 14 days
use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k
= 0.693/(half life)
= 0.693/(14)
= 4.95*10^-2 days-1
we have:
[P]o = 8.0 g
t = 98.0 days
k = 4.95*10^-2 days-1

use integrated rate law for 1st order reaction
ln[P] = ln[P]o - k*t
ln[P] = ln(8) - 4.95*10^-2*98
ln[P] = 2.0794 - 4.95*10^-2*98
ln[P] = -2.7716
[P] = 6.256*10^-2 g
Answer: 6.256*10^-2 g

B)
In each half life the concentration decreases by half

So, here concentration is decreasing to 1/4
So, it must takes 2 half lifes

time = 2*5730 years
=11460 years

Answer: 11460 years

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