Given, mass of a neutron `=1 .00866u,` mass of a proton `= 1.00727u,` mass of `{:(16), (8):}O = 15. 99053u.` Then, the energy required to separate `{:(16),(8):}O` into its constituents is

Options

A. `12.7`
B. cannot be estimated from given data
C. `1.49 xx 10 ^(-10)J`
D. `127. 5 MeV`

Answer

To solve the problem of finding the energy required to separate \(^{16}_{8}O\) into its constituents, we will follow these steps:

### Step 1: Identify the constituents of \(^{16}_{8}O\)
The nucleus of oxygen-16 consists of:
- 8 protons
- 8 neutrons

### Step 2: Calculate the total mass of the constituents
We will calculate the total mass of the 8 protons and 8 neutrons using their respective masses:
- Mass of one proton = \(1.00727 \, u\)
- Mass of one neutron = \(1.00866 \, u\)

Total mass of 8 protons:
\[ \text{Mass of protons} = 8 \times 1.00727 \, u = 8.05816 \, u \]

Total mass of 8 neutrons:
\[ \text{Mass of neutrons} = 8 \times 1.00866 \, u = 8.06928 \, u \]

### Step 3: Calculate the combined mass of the constituents
Now, we add the mass of the protons and the mass of the neutrons:
\[ \text{Total mass of constituents} = 8.05816 \, u + 8.06928 \, u = 16.12744 \, u \]

### Step 4: Calculate the mass defect
The mass defect (\(\Delta m\)) is the difference between the mass of the constituents and the actual mass of the oxygen nucleus:
\[ \Delta m = \text{Total mass of constituents} - \text{Mass of } ^{16}_{8}O \]
Given that the mass of \(^{16}_{8}O\) is \(15.99053 \, u\):
\[ \Delta m = 16.12744 \, u - 15.99053 \, u = 0.13691 \, u \]

### Step 5: Convert mass defect to energy
Using Einstein's mass-energy equivalence \(E = \Delta m c^2\), where \(c^2\) is equivalent to \(931 \, \text{MeV/u}\):
\[ E = 0.13691 \, u \times 931 \, \text{MeV/u} = 127.5 \, \text{MeV} \]

### Conclusion
The energy required to separate \(^{16}_{8}O\) into its constituents is approximately **127.5 MeV**.

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