Find the `Q` value of the reaction `P + .^(7) Li rarr .^(4) He +.^(4) He`. Determine whether the reaction is exothermic or endothermic. The atomic masses of `.^(1) Hp,.^(4) He` and `.^(7)Li` are `1.007825 u,4.002603 u`, and `7.016004 u`, respectively.

Options

A. (a)17.35 MeV
B. (b)18.06 MeV
C. (c)177.35 MeV
D. (d)170.35 MeV

Answer

To find the Q value of the reaction \( P + ^{7}\text{Li} \rightarrow ^{4}\text{He} + ^{4}\text{He} \) and determine whether the reaction is exothermic or endothermic, we will follow these steps:

### Step 1: Identify the masses of the reactants and products
The atomic masses provided are:
- Mass of proton \( (P) \): \( 1.007825 \, u \)
- Mass of lithium \( (^{7}\text{Li}) \): \( 7.016004 \, u \)
- Mass of helium \( (^{4}\text{He}) \): \( 4.002603 \, u \)

### Step 2: Calculate the total mass of the reactants
The total mass of the reactants is the sum of the masses of the proton and lithium:
\[ m_R = m_P + m_{^{7}\text{Li}} = 1.007825 \, u + 7.016004 \, u = 8.023829 \, u \]

### 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:
\[ m_P = 2 \times m_{^{4}\text{He}} = 2 \times 4.002603 \, u = 8.005206 \, u \]

### Step 4: Calculate the mass defect \( \Delta m \)
The mass defect \( \Delta m \) is given by:
\[ \Delta m = m_R - m_P = 8.023829 \, u - 8.005206 \, u = 0.018623 \, u \]

### Step 5: Convert the mass defect to energy (Q value)
Using Einstein's equation \( Q = \Delta m c^2 \), we need to convert the mass defect from atomic mass units to energy. The conversion factor is:
\[ 1 \, u \approx 931.5 \, \text{MeV} \]
Thus,
\[ Q = \Delta m \times 931.5 \, \text{MeV} = 0.018623 \, u \times 931.5 \, \text{MeV/u} \approx 17.35 \, \text{MeV} \]

### Step 6: Determine if the reaction is exothermic or endothermic
Since the Q value is positive (\( Q = 17.35 \, \text{MeV} \)), this indicates that energy is released during the reaction. Therefore, the reaction is exothermic.

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

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