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