If the amount of carbon-14 in the original sample had been 48 grams, 6 gm carbon-14 would have been left after 17,100 years
Half-life
The amount of time required for a quantity to fall to half its value as measured at the beginning of the time period.
The half-life (t½) of C-14 is 5700 years, which means that after 5700 years half of the sample would have decayed and half would be left as it is.
- After 5700 years ( first half-life)
[tex]\frac{48}{2} = 24[/tex] mg decays and 24 g remains left.
- After another 5700 years ( two half-lives or 11400 years)
[tex]\frac{24}{2} = 12[/tex] mg decays and 12 g remains left.
- After another 5700 years ( three half-lives or 17100 years)
[tex]\frac{12}{2} = 6[/tex] mg decays and 6 g remains left.
Thus, after three half-lives or 17100 years, 6 g of C-14 will be left.
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