Calculate the Q-values of the fusion reaction
`He^4+He^4 = Be^8`
In such a fusion energetically favourable? Atomic mass of `Be^8` is 8.0053u and that of `He^4`is 4.0026 u.

Explanation

To calculate the Q-value of the fusion reaction \( \text{He}^4 + \text{He}^4 \rightarrow \text{Be}^8 \), we will follow these steps:

### Step 1: Identify the masses involved in the reaction
We have:
- Mass of \( \text{He}^4 \) (Helium) = 4.0026 u
- Mass of \( \text{Be}^8 \) (Beryllium) = 8.0053 u

### Step 2: Calculate the total initial mass
Since we have two helium nuclei, the total initial mass is:
\[ \text{Total initial mass} = 2 \times \text{Mass of He}^4 = 2 \times 4.0026 \, \text{u} = 8.0052 \, \text{u} \]

### Step 3: Calculate the change in mass (Δm)
The change in mass (Δm) for the reaction can be calculated as:
\[ \Delta m = \text{Total initial mass} - \text{Mass of Be}^8 \]
Substituting the values:
\[ \Delta m = 8.0052 \, \text{u} - 8.0053 \, \text{u} = -0.0001 \, \text{u} \]

### Step 4: Convert the change in mass to energy (Q-value)
The energy released (Q-value) can be calculated using the formula:
\[ Q = \Delta m \times c^2 \]
Where \( c^2 \) in terms of MeV can be expressed as:
\[ 1 \, \text{u} \approx 931 \, \text{MeV} \]
Thus,
\[ Q = -0.0001 \, \text{u} \times 931 \, \text{MeV/u} = -0.0931 \, \text{MeV} \]

### Step 5: Convert MeV to keV
To express the Q-value in kilo-electron volts (keV):
\[ Q = -0.0931 \, \text{MeV} \times 1000 = -93.1 \, \text{keV} \]

### Step 6: Determine if the reaction is energetically favorable
Since the Q-value is negative, this indicates that the reaction is not energetically favorable.

### Final Result
The Q-value of the fusion reaction \( \text{He}^4 + \text{He}^4 \rightarrow \text{Be}^8 \) is:
\[ Q = -93.1 \, \text{keV} \]
Thus, the reaction is not energetically favorable.

---