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

`2.8977* 10^(-4) g` of mass is converted to energy.

Step-by-step explanation:

Mass of 1 mole of carbon-11 = 11 g

Moles of carbon-11 in 1 gram :

`(1 g)/(11 g/mol)=0.0909 mol`

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

`E=2.87* 10^(11) J`

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

`E'=E* 0.0909=2.87* 10^(11) J* 0.0909 mol=2.608* 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* 10^(10) J=m* (3* 10^8 m/s)^2`

m =
`2.8977* 10^(-7) kg=2.8977* 10^(-4) g`

`2.8977* 10^(-4) g` of mass is converted to energy.

Answer 2

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