8 protons and 8 lectures are separately at rest. How much energy will be released if we form `_^16O_8` nucleus?
Given:
Mass of `_^16O_8` atom = 15.994915u
Mass of neutron =1.008665u
Mass of hydrogen atom = 1.007825u

Explanation

To solve the problem of how much energy is released when 8 protons and 8 neutrons combine to form the `^16O_8` nucleus, we can follow these steps:

### Step 1: Calculate the total mass of the initial particles
We have 8 protons and 8 neutrons. The mass of a proton is given as the mass of a hydrogen atom (since a hydrogen atom consists of one proton and one electron, we can approximate the mass of a proton as the mass of the hydrogen atom for this calculation).

- Mass of a proton (hydrogen atom) = 1.007825 u
- Mass of a neutron = 1.008665 u

Total mass of 8 protons:
\[ \text{Mass of protons} = 8 \times 1.007825 \, \text{u} = 8.0626 \, \text{u} \]

Total mass of 8 neutrons:
\[ \text{Mass of neutrons} = 8 \times 1.008665 \, \text{u} = 8.06932 \, \text{u} \]

Total initial mass (mass of protons + mass of neutrons):
\[ \text{Total initial mass} = 8.0626 \, \text{u} + 8.06932 \, \text{u} = 16.13192 \, \text{u} \]

### Step 2: Find the mass of the `^16O_8` nucleus
The mass of the `^16O_8` nucleus is given as:
\[ \text{Mass of } ^{16}O_8 = 15.994915 \, \text{u} \]

### Step 3: Calculate the mass defect
The mass defect (Δm) is the difference between the total initial mass and the mass of the nucleus formed:
\[ \Delta m = \text{Total initial mass} - \text{Mass of } ^{16}O_8 \]
\[ \Delta m = 16.13192 \, \text{u} - 15.994915 \, \text{u} = 0.137005 \, \text{u} \]

### Step 4: Convert the mass defect to energy
Using Einstein's equation \(E = \Delta m c^2\), we can convert the mass defect into energy. The energy equivalent of 1 atomic mass unit (u) is approximately 931.5 MeV.

\[ E = \Delta m \times 931.5 \, \text{MeV/u} \]
\[ E = 0.137005 \, \text{u} \times 931.5 \, \text{MeV/u} \approx 127.62 \, \text{MeV} \]

### Conclusion
The energy released when 8 protons and 8 neutrons combine to form the `^16O_8` nucleus is approximately **127.62 MeV**.

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