Answer to Question #133372 in Molecular Biology for E’Mya Jones

Question #133372
A living 120-pound woman contains about 6 x 10 grams of carbon-14. How many grams of carbon-14 would remain after 17100 years? What has happened to the rest of the carbon-14? (Assume carbon-14 is a beta emitter with a half-life of 5700 years.)
1
Expert's answer
2020-09-16T07:52:13-0400

Half-life (t1/2)is the time it can take for half the mass of a radio-active isotope to undergo decay.

Since for carbon-14 this time is given as 5700 years; then it follows that after this period, any mass of carbon-14 would have decayed, and only half of it will remain.

In simple terms:

After 17100 years, the number of half-lifes for carbon-14 are:


This then means;

For the first half-life; (30g will decay and 30g remain)


For the second, (15g decay and 15 remain)


For the third; (7.5g decay and 7.5 remain)

Thus after 17100 years, 7.5 g of the initial 60g will remain.


When carbon-14 undergoes decay, it is called a beta decay because it emits an electron and an electron antineutrino.


14C 14N +e- + ve-

One of the neutrons become a proton and the carbon-14 decays into a stable(non-radio-active) isotope nitrogen-14

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