A heavy nuleus having mass number `200` gets disintegrated into two small fragmnets of mass numbers `80` and `120`. If binding energy per nulceon for parent atom is `6.5 MeV` and for daughter nuceli is `7 MeV` and `8 MeV`, respectivley , then the energy released in the decay will be.

Options

A. 200 MeV
B. (-)220 MeV
C. 220 MeV
D. 180 MeV

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the Binding Energy of the Parent Nucleus
The binding energy of the parent nucleus can be calculated using the formula:
\[ \text{Binding Energy}_{\text{parent}} = \text{Binding Energy per Nucleon} \times \text{Mass Number} \]
Given that the binding energy per nucleon for the parent nucleus is \(6.5 \, \text{MeV}\) and the mass number is \(200\):
\[ \text{Binding Energy}_{\text{parent}} = 6.5 \, \text{MeV} \times 200 = 1300 \, \text{MeV} \]

### Step 2: Calculate the Binding Energy of the Daughter Nuclei
Next, we calculate the binding energy for each daughter nucleus.

For the first daughter nucleus (mass number \(80\), binding energy per nucleon \(7 \, \text{MeV}\)):
\[ \text{Binding Energy}_{\text{daughter 1}} = 7 \, \text{MeV} \times 80 = 560 \, \text{MeV} \]

For the second daughter nucleus (mass number \(120\), binding energy per nucleon \(8 \, \text{MeV}\)):
\[ \text{Binding Energy}_{\text{daughter 2}} = 8 \, \text{MeV} \times 120 = 960 \, \text{MeV} \]

### Step 3: Calculate the Total Binding Energy of the Daughter Nuclei
Now, we sum the binding energies of the two daughter nuclei:
\[ \text{Total Binding Energy}_{\text{daughters}} = \text{Binding Energy}_{\text{daughter 1}} + \text{Binding Energy}_{\text{daughter 2}} = 560 \, \text{MeV} + 960 \, \text{MeV} = 1520 \, \text{MeV} \]

### Step 4: Calculate the Energy Released in the Decay
The energy released during the decay can be found by subtracting the binding energy of the parent nucleus from the total binding energy of the daughter nuclei:
\[ \text{Energy Released} = \text{Total Binding Energy}_{\text{daughters}} - \text{Binding Energy}_{\text{parent}} \]
Substituting the values we calculated:
\[ \text{Energy Released} = 1520 \, \text{MeV} - 1300 \, \text{MeV} = 220 \, \text{MeV} \]

### Final Answer
The energy released in the decay is \(220 \, \text{MeV}\).

---