What is the Q-value of the reaction?
`""^(1)H+""^(7)Lito ""^(4)He+""^(4)He`
The atomic masses of `""^(1)H,""^(4)Heand ""^(7)Li` 1.007825u, 4.0026034u and 7.01600u, respectively.

Options

A. `17.35` Me V
B. `18.06` Me V
C. `177.35` Me V
D. `170.35` Me V

Explanation

To find the Q-value of the nuclear reaction \( ^{1}\text{H} + ^{7}\text{Li} \rightarrow 2 \, ^{4}\text{He} \), we will follow these steps:

### Step 1: Identify the atomic masses
We have the following atomic masses:
- Mass of \( ^{1}\text{H} = 1.007825 \, u \)
- Mass of \( ^{7}\text{Li} = 7.01600 \, u \)
- Mass of \( ^{4}\text{He} = 4.0026034 \, u \)

### Step 2: Calculate the total mass of the reactants
The total mass of the reactants is the sum of the masses of hydrogen and lithium:
\[ \text{Mass of reactants} = m(^{1}\text{H}) + m(^{7}\text{Li}) = 1.007825 \, u + 7.01600 \, u = 8.023825 \, u \]

### Step 3: Calculate the total mass of the products
The total mass of the products is the sum of the masses of the two helium nuclei:
\[ \text{Mass of products} = 2 \times m(^{4}\text{He}) = 2 \times 4.0026034 \, u = 8.0052068 \, u \]

### Step 4: Calculate the mass defect
The mass defect (\( \Delta m \)) is the difference between the total mass of the reactants and the total mass of the products:
\[ \Delta m = \text{Mass of reactants} - \text{Mass of products} = 8.023825 \, u - 8.0052068 \, u = 0.0186182 \, u \]

### Step 5: Convert the mass defect to energy (Q-value)
The Q-value can be calculated using the formula:
\[ Q = \Delta m \times 931.5 \, \text{MeV/u} \]
Substituting the mass defect:
\[ Q = 0.0186182 \, u \times 931.5 \, \text{MeV/u} \approx 17.35 \, \text{MeV} \]

### Final Answer
The Q-value of the reaction is approximately \( 17.35 \, \text{MeV} \).

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