In a nuclear fusion process, two deuterium nuclei (\text{^{2}_{1}H}) fuse to form a helium… — JAMB UTME

In a nuclear fusion process, two deuterium nuclei (

\text{^{2}_{1}H}

) fuse to form a helium-3 nucleus (

\text{^{3}_{2}He}

) and a neutron (

\text{^{1}_{0}n}

) according to the reaction equation:

\text{^{2}_{1}H} + \text{^{2}_{1}H} \rightarrow \text{^{3}_{2}He} + \text{^{1}_{0}n} + Q

Given the mass values:
- Mass of $\text{^{2}_{1}H} = 2.0141\text{ u}$
- Mass of $\text{^{3}_{2}He} = 3.0160\text{ u}$
- Mass of $\text{^{1}_{0}n} = 1.0087\text{ u}$

Using the conversion factor $1\text{ u} = 931.5\text{ MeV}$ , what is the energy released ( $Q$ ) in this fusion reaction in $\text{MeV}$ ?

Cevap: 3.26 MeV

Cevap

The total energy released (

Q

) in the reaction is

3.26\text{ MeV}

The energy released in a nuclear fusion reaction is proportional to the decrease in total rest mass (mass defect). Summing the mass of two deuterium nuclei gives

4.0282\text{ u}

, while the sum of the product masses (

\text{^{3}_{2}He}

and a neutron) is

4.0247\text{ u}

. Subtracting these yields a mass defect of

0.0035\text{ u}

. Multiplying

0.0035\text{ u}

931.5\text{ MeV/u}

gives

3.26\text{ MeV}

of released energy.

Adım Adım Çözüm

Calculate the total initial mass of the reacting deuterium nuclei.

m_{\text{reactants}} = 2 \times 2.0141\text{ u} = 4.0282\text{ u}

Two deuterium nuclei participate on the reactant side of the equation.

Calculate the total final mass of the products.

m_{\text{products}} = 3.0160\text{ u} + 1.0087\text{ u} = 4.0247\text{ u}

The reaction produces one helium-3 nucleus and one neutron.

Determine the mass defect (difference between reactant and product masses).

\Delta m = 4.0282\text{ u} - 4.0247\text{ u} = 0.0035\text{ u}

The mass lost during fusion is converted into nuclear kinetic energy and radiation.

Convert the mass defect into energy in MeV using the conversion factor.

Q = 0.0035\text{ u} \times 931.5\text{ MeV/u} = 3.26025\text{ MeV} \approx 3.26\text{ MeV}

Each atomic mass unit lost corresponds to

931.5\text{ MeV}

of energy.

Anahtar Kavram

Mass defect and energy release in nuclear fusion reactions (

E = \Delta m c^2

)

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