Question

Carbon-11 decays by positron emission: 116c → 115b + 01e the decay occurs with a release of 2.87 ⋅ 1011 j per mole of carbon-11. When 1.00 g of carbon-11 undergoes this radioactive decay, ________ g of mass is converted to energy.

Answer 1

116c → 115b + 01e

As per equation, one mole of carbon gives one mole of boron which gives 2.87 X 10^11 joules of energy.

Now the mass of one mole of given carbon isotope is 11g / mole

Thus the energy releases from isotope is from 11 grams of carbon

The energy released from 1 gram = 2.87 X 10^11 joules  / 11 = 2.61 X 10^10 Joules of energy

Answer 2

Answer:

$2.8977\times 10^{-4} g$ of mass is converted to energy.

Explanation:

Mass of 1 mole of carbon-11 = 11 g

Moles of carbon-11 in 1 gram :

$\frac{1 g}{11 g/mol}=0.0909 mol$

Energy released when 1 mol of carbon-111 undergoes positron emission: E

$E=2.87\times 10^{11} J$

Then energy released when 0.0909 moles of carbon-11 undergoes positron emission:

$E'=E\times 0.0909=2.87\times 10^{11} J\times 0.0909 mol=2.608\times 10^{10} J$

Let the mass converted into energy during the process be m

Using Einstein equation of energy:

$E=mc^2$

E = energy released

m = mass converted into energy

c = speed of the light

$2.608\times 10^{10} J=m\times (3\times 10^8 m/s)^2$

m = $2.8977\times 10^{-7} kg=2.8977\times 10^{-4} g$

$2.8977\times 10^{-4} g$ of mass is converted to energy.