It is believed that two carbon-12 nuclei can react in the core of a supergiant star to form sodium-23 and hydrogen-1. Calculate the energy released from this reaction for each mole of hydrogen formed. Na + H C+C Particle Mass (amu) C-12 12.000000 Na-23 22.989767 H-1 1.007825 (1 kg = 6.022 x 1026 amu; NA = 6.022 x 1023 mol-1. c=2.99792458 x 108 m/s)

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**Title: Nuclear Reaction in Supergiant Stars**

It is believed that two carbon-12 nuclei can react in the core of a supergiant star to form sodium-23 and hydrogen-1. Calculate the energy released from this reaction for each mole of hydrogen formed.

**Nuclear Reaction Equation:**

\[ \, _{6}^{12}\text{C} + \, _{6}^{12}\text{C} \rightarrow \, _{11}^{23}\text{Na} + \, _{1}^{1}\text{H} \]

**Particle Mass (amu):**
- Carbon-12: 12.000000
- Sodium-23: 22.989767
- Hydrogen-1: 1.007825

**Constants:**
- 1 kg = 6.022 × 10²⁶ amu
- Avogadro's Number (\(N_A\)) = 6.022 × 10²³ mol⁻¹
- Speed of Light (\(c\)) = 2.99792458 × 10⁸ m/s

### Explanation

In this reaction, the fusion of two carbon-12 nuclei results in the formation of sodium-23 and a proton (hydrogen-1). The masses are provided in atomic mass units (amu), and calculation of the energy released involves using the mass-energy equivalence principle. These reactions are typical in high-temperature environments, such as the cores of supergiant stars, and are crucial in the process of nucleosynthesis.
Transcribed Image Text:**Title: Nuclear Reaction in Supergiant Stars** It is believed that two carbon-12 nuclei can react in the core of a supergiant star to form sodium-23 and hydrogen-1. Calculate the energy released from this reaction for each mole of hydrogen formed. **Nuclear Reaction Equation:** \[ \, _{6}^{12}\text{C} + \, _{6}^{12}\text{C} \rightarrow \, _{11}^{23}\text{Na} + \, _{1}^{1}\text{H} \] **Particle Mass (amu):** - Carbon-12: 12.000000 - Sodium-23: 22.989767 - Hydrogen-1: 1.007825 **Constants:** - 1 kg = 6.022 × 10²⁶ amu - Avogadro's Number (\(N_A\)) = 6.022 × 10²³ mol⁻¹ - Speed of Light (\(c\)) = 2.99792458 × 10⁸ m/s ### Explanation In this reaction, the fusion of two carbon-12 nuclei results in the formation of sodium-23 and a proton (hydrogen-1). The masses are provided in atomic mass units (amu), and calculation of the energy released involves using the mass-energy equivalence principle. These reactions are typical in high-temperature environments, such as the cores of supergiant stars, and are crucial in the process of nucleosynthesis.
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