(a) One such reaction fuses two nuclei of carbon-12 (12/6C ) to form an atom

of neon (20/10Ne ) with the emission of an α-particle. Write an equation for
this process, indicating the atomic number and mass number of each of
the products in the usual way.
(b) Another reaction involving carbon-12 in stars is one in which a
carbon-12 nucleus fuses with a hydrogen nucleus (atomic mass of 1) to
form a nucleus of nitrogen, releasing 1.95 MeV in the process.
Write down the equation for this process, and using values for the
binding energy of the hydrogen and carbon-12 nuclei of 0 MeV and
–92.2 MeV respectively, calculate the binding energy of the nitrogen
nucleus. (Show all your working.)
(c) Convert the energy liberated in the reaction in part (b) into the
equivalent amount of energy in joules, and then calculate the amount of
mass that has been converted into energy as a result of this process.
Using SI units throughout show that the units for the mass are
kilograms.
(Express your answers in scientific notation to an appropriate number of
significant figures.)

(a) The equation for the fusion reaction of carbon-12 to form neon-20 with the emission of an alpha particle is:

^12/6C + ^4/2He → ^20/10Ne + ^4/2He

(b) The equation for the fusion reaction of carbon-12 and hydrogen to form nitrogen with the release of 1.95 MeV is:

^12/6C + ^1/1H → ^13/7N + ^4/2He

To calculate the binding energy of the nitrogen nucleus, we need to subtract the binding energy of the reactants from the binding energy of the products. The binding energy is calculated using the formula:

Binding Energy = Mass Defect x c^2

First, let's calculate the mass defect for carbon-12 and hydrogen:

Mass Defect of carbon-12 = (12.000000 - 6.644657) amu = 5.355343 amu
Mass Defect of hydrogen = (1.007825 - 1.007825) amu = 0 amu

Next, calculate the binding energy for carbon-12 and hydrogen:

Binding Energy of carbon-12 = 5.355343 amu x (1.66053906660 x 10^-27 kg/amu) x (299792458 m/s)^2 = -92.2 MeV
Binding Energy of hydrogen = 0 amu x (1.66053906660 x 10^-27 kg/amu) x (299792458 m/s)^2 = 0 MeV

Now, let's calculate the binding energy of the nitrogen nucleus:

Binding Energy of nitrogen = (Mass Defect of nitrogen x c^2) + Binding Energy of carbon-12 + Binding Energy of hydrogen
= (0.998623 - 0.998623) amu x (1.66053906660 x 10^-27 kg/amu) x (299792458 m/s)^2 + (-92.2 MeV) + (0 MeV)
= 0 MeV + (-92.2 MeV) + (0 MeV)
= -92.2 MeV

Therefore, the binding energy of the nitrogen nucleus is -92.2 MeV.

(c) To convert the energy liberated in the reaction in part (b) into joules, we can use the conversion factor that 1 MeV = 1.602176634 x 10^-13 J.

Energy liberated = 1.95 MeV x (1.602176634 x 10^-13 J/MeV) = 3.1237422913 x 10^-13 J

To calculate the equivalent mass, we use Einstein's mass-energy equivalence formula:

Energy = (mass change) x c^2

Rearranging the formula, we can solve for the mass change:

Mass change = Energy / c^2 = 3.1237422913 x 10^-13 J / (299792458 m/s)^2

Mass change = 3.47894891 x 10^-30 kg

Therefore, the amount of mass that has been converted into energy as a result of this process is 3.47894891 x 10^-30 kg.

(a) The reaction in which two nuclei of carbon-12 (12/6C) fuse to form an atom of neon (20/10Ne) with the emission of an α-particle can be written as:

12/6C + 12/6C -> 20/10Ne + 4/2He

In this equation, the atomic number and mass number of each product are indicated as subscripts and superscripts respectively.

(b) The reaction where a carbon-12 nucleus fuses with a hydrogen nucleus to form a nucleus of nitrogen with the release of 1.95 MeV of energy can be written as:

12/6C + 1/1H -> 14/7N + 1.95 MeV

To calculate the binding energy of the nitrogen nucleus, we can use the concept of mass-energy equivalence. The binding energy (E) of a nucleus is given by the equation:

E = (Δm)c^2

Where Δm is the change in mass, c is the speed of light.

The binding energy (E) of the nitrogen nucleus can be calculated as follows:

E = (m_initial - m_final)c^2

Given that the binding energy of hydrogen is 0 MeV and the binding energy of carbon-12 is -92.2 MeV, we can substitute these values into the equation:

ΔE = (0 MeV + (-92.2 MeV))c^2
ΔE = -92.2 MeV c^2

(c) To convert the energy liberated in the reaction (part b) into joules, we need to use the conversion factor between electron volts (eV) and joules (J). The conversion factor is 1 eV = 1.6 x 10^-19 J.

So, the energy liberated in the reaction is:
1.95 MeV x (1.6 x 10^-19 J/eV) = 3.12 x 10^-19 J

To calculate the amount of mass converted into energy, we can use Einstein's mass-energy equivalence equation:

E = mc^2

Where E is the energy liberated, m is the mass converted, and c is the speed of light.

We can rearrange the equation to solve for mass (m):

m = E / c^2

Substituting the value of energy (3.12 x 10^-19 J) and the value of the speed of light (3 x 10^8 m/s), we can calculate the mass converted:

m = (3.12 x 10^-19 J) / (3 x 10^8 m/s)^2
m = (3.12 x 10^-19 J) / (9 x 10^16 m^2/s^2)
m = 3.47 x 10^-35 kg

Therefore, the amount of mass converted into energy as a result of this process is 3.47 x 10^-35 kg when using SI units throughout.