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.)

Expert's answer

Half-life (t_{1/2})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:

"=\\dfrac{17100}{5700} = 3 half-lifes"

This then means;

For the first half-life; "\\dfrac{1}{2}x60g =30g" (30g will decay and 30g remain)

For the second, "\\dfrac{1}{2}x30 = 15g" (15g decay and 15 remain)

For the third; "\\dfrac{1}{2}x15 = 7.5g" (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.

^{14}C "\\to" ^{14}N +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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