Calculate the Q - value of the reaction
`._(1)H^(2)+._(1)H^(2) rarr ._(1)H^(3)+._(1)H^(1)`
`m(._(1)H^(2))=2.014103 "amu" m(._(1)H^(3))=3.016049 "amu" m(._(1H^(1))=1.007825` amu

Answer

To calculate the Q-value of the reaction \( _{1}^{2}H + _{1}^{2}H \rightarrow _{1}^{3}H + _{1}^{1}H \), we will follow these steps:

### Step 1: Write down the masses involved in the reaction
We have the following masses:
- Mass of deuterium (\( _{1}^{2}H \)): \( m( _{1}^{2}H ) = 2.014103 \, \text{amu} \)
- Mass of tritium (\( _{1}^{3}H \)): \( m( _{1}^{3}H ) = 3.016049 \, \text{amu} \)
- Mass of hydrogen (\( _{1}^{1}H \)): \( m( _{1}^{1}H ) = 1.007825 \, \text{amu} \)

### Step 2: Set up the Q-value equation
The Q-value can be calculated using the formula:
\[ Q = \left( \text{Total mass of reactants} - \text{Total mass of products} \right) \times c^2 \]
Where \( c^2 \) is a conversion factor, \( c^2 = 931.5 \, \text{MeV/amu} \).

### Step 3: Calculate the total mass of reactants
The total mass of the reactants (2 deuterium nuclei) is:
\[ \text{Total mass of reactants} = 2 \times m( _{1}^{2}H ) = 2 \times 2.014103 \, \text{amu} = 4.028206 \, \text{amu} \]

### Step 4: Calculate the total mass of products
The total mass of the products (1 tritium nucleus and 1 hydrogen nucleus) is:
\[ \text{Total mass of products} = m( _{1}^{3}H ) + m( _{1}^{1}H ) = 3.016049 \, \text{amu} + 1.007825 \, \text{amu} = 4.023874 \, \text{amu} \]

### Step 5: Calculate the mass defect
The mass defect is given by:
\[ \text{Mass defect} = \text{Total mass of reactants} - \text{Total mass of products} \]
Substituting the values:
\[ \text{Mass defect} = 4.028206 \, \text{amu} - 4.023874 \, \text{amu} = 0.004332 \, \text{amu} \]

### Step 6: Calculate the Q-value
Now, substituting the mass defect into the Q-value equation:
\[ Q = \text{Mass defect} \times c^2 = 0.004332 \, \text{amu} \times 931.5 \, \text{MeV/amu} \]
Calculating this gives:
\[ Q = 0.004332 \times 931.5 \approx 4.033 \, \text{MeV} \]

### Final Answer
The Q-value of the reaction is approximately \( 4.033 \, \text{MeV} \).

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