Binding energies of `._1H^2 , ._2He^4 , ._26Fe^56` and `._92U^235` nuclei are 2.22Mev, 28.4Mev, 492Mev and 1786MeV respectively which one of the following is more stable?

Options

A. `._1H^2`
B. `._2He^4`
C. `._26 Fe^56`
D. `._92U^235`

Answer

To determine which nucleus is the most stable based on the given binding energies, we will calculate the binding energy per nucleon for each of the nuclei provided. The nucleus with the highest binding energy per nucleon will be the most stable.

### Step-by-Step Solution:

1. **Identify the Binding Energies and Nucleon Counts:**
- Hydrogen (H): Binding energy = 2.22 MeV, Number of nucleons = 2
- Helium (He): Binding energy = 28.4 MeV, Number of nucleons = 4
- Iron (Fe): Binding energy = 492 MeV, Number of nucleons = 56
- Uranium (U): Binding energy = 1786 MeV, Number of nucleons = 235

2. **Calculate Binding Energy per Nucleon:**
- For Hydrogen:
\[ \text{Binding energy per nucleon} = \frac{2.22 \text{ MeV}}{2} = 1.11 \text{ MeV/nucleon} \]
- For Helium:
\[ \text{Binding energy per nucleon} = \frac{28.4 \text{ MeV}}{4} = 7.1 \text{ MeV/nucleon} \]
- For Iron:
\[ \text{Binding energy per nucleon} = \frac{492 \text{ MeV}}{56} = 8.78 \text{ MeV/nucleon} \]
- For Uranium:
\[ \text{Binding energy per nucleon} = \frac{1786 \text{ MeV}}{235} \approx 7.6 \text{ MeV/nucleon} \]

3. **Compare the Binding Energies per Nucleon:**
- Hydrogen: 1.11 MeV/nucleon
- Helium: 7.1 MeV/nucleon
- Iron: 8.78 MeV/nucleon
- Uranium: 7.6 MeV/nucleon

4. **Determine the Most Stable Nucleus:**
- The nucleus with the highest binding energy per nucleon is Iron (Fe) with 8.78 MeV/nucleon.

### Conclusion:
The most stable nucleus among the given options is Iron (Fe).