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.

Answer

To find the energy released in the decay of a heavy nucleus, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass number of the parent nucleus (A) = 200
- Mass number of the first daughter nucleus (A1) = 80
- Mass number of the second daughter nucleus (A2) = 120
- Binding energy per nucleon of the parent nucleus (BE_parent) = 6.5 MeV
- Binding energy per nucleon of the first daughter nucleus (BE_daughter1) = 7 MeV
- Binding energy per nucleon of the second daughter nucleus (BE_daughter2) = 8 MeV

2. **Calculate the total binding energy of the parent nucleus:**
\[ BE_{parent} = BE_{per nucleon} \times A = 6.5 \, \text{MeV} \times 200 = 1300 \, \text{MeV} \]

3. **Calculate the total binding energy of the daughter nuclei:**
\[ BE_{daughter1} = BE_{per nucleon} \times A1 = 7 \, \text{MeV} \times 80 = 560 \, \text{MeV} \]
\[ BE_{daughter2} = BE_{per nucleon} \times A2 = 8 \, \text{MeV} \times 120 = 960 \, \text{MeV} \]
\[ BE_{daughters\ total} = BE_{daughter1} + BE_{daughter2} = 560 \, \text{MeV} + 960 \, \text{MeV} = 1520 \, \text{MeV} \]

4. **Calculate the energy released in the decay:**
\[ Energy\ released = BE_{daughters\ total} - BE_{parent} \]
\[ Energy\ released = 1520 \, \text{MeV} - 1300 \, \text{MeV} = 220 \, \text{MeV} \]

### Final Answer:
The energy released in the decay is **220 MeV**.

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