Carbon-11 decays by positron emission: C → B + e The decay occurs with a release of 2.87 × 10¹¹ J per mole of carbon-11. When 4.00 g of carbon-11 undergoes this radioactive decay, __________ g of mass is converted to energy.

Question

Quizplus · Accepted Answer

We can use Einstein's famous equation E = mc² to calculate the amount of mass that is converted to energy during the radioactive decay of 4.00 g of carbon-11.
First, we need to find the total energy released during the decay:
2.87 × 10¹⁰ J/mol × (4.00 g / 12.01 g/mol) = 9.54 × 10⁸ J
This is the amount of energy released when one mole of carbon-11 undergoes radioactive decay. To find the amount of mass converted to energy, we divide this energy by the speed of light squared:
9.54 × 10⁸ J / (3.00 × 10⁸ m/s)² = 1.06 × 10⁻² g
Therefore, the answer is A, 1.16 × 10⁻³ g (rounded to three significant figures).

Carbon-11 Decays by Positron Emission: C → B