In proton-proton cycle, four hydrogen atoms combine to release energy

Options

A. 2.67 MeV
B. 2.67 KeV
C. 26.7 MeV
D. 26.7 KeV

Answer

To solve the problem regarding the proton-proton cycle and the energy released when four hydrogen atoms combine, we can break it down into a series of steps:

### Step 1: Understanding the Proton-Proton Cycle
The proton-proton cycle is a series of nuclear reactions that occur in stars, including our Sun. It starts with hydrogen nuclei (protons) and ultimately produces helium nuclei, releasing energy in the process.

### Step 2: Initial Reaction
In the first step of the proton-proton cycle, two protons (hydrogen nuclei) combine to form a deuterium nucleus (which consists of one proton and one neutron) along with the emission of a positron and a neutrino. The reaction can be represented as:
\[ 1H^1 + 1H^1 \rightarrow 2H^1 + e^+ + \nu_e \]
This reaction releases energy of about 0.42 MeV.

### Step 3: Formation of Helium-3
In the next step, the deuterium nucleus can combine with another proton to form helium-3:
\[ 2H^1 + 1H^1 \rightarrow 3He^2 + \gamma \]
This step also releases energy, contributing to the overall energy output of the cycle.

### Step 4: Final Reaction
Two helium-3 nuclei can then combine to form helium-4 and release two protons:
\[ 3He^2 + 3He^2 \rightarrow 4He^4 + 2(1H^1) \]
This step releases a significant amount of energy, contributing to the total energy released in the cycle.

### Step 5: Total Energy Calculation
The total energy released in the proton-proton cycle when four hydrogen nuclei are converted into one helium nucleus can be calculated by summing the energies released in each step. The total energy released is approximately:
\[ E_{total} \approx 26.7 \text{ MeV} \]

### Conclusion
Thus, when four hydrogen atoms combine in the proton-proton cycle, they release a total energy of approximately 26.7 MeV.

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