Chapter 8, Problem 1QQ

Choose the best answer to each of the following. Explain your reasoning.

at the center of the star fusion convert hydrogen into (a) plasma (b) radiation and elements like carbon and nitrogen (c) Helium and energy

To determine

The products of conversion of Hydrogen due to fusion at the center of the Sun.

Answer to Problem 1QQ

At the center of the Sun, fusion converts hydrogen into (c) helium and energy.

Explanation of Solution

Introduction:

The temperature of the Sun's core is around 14 million Kelvin. At this temperature, the hydrogen in the core exists as ionized plasma. Due to the high temperature, the protons (Hydrogen ions) acquire extremely large kinetic energies. As a result, when they collide, the protons overcome the electrostatic repulsion and come close enough for the strong force to take charge and the protons fuse together to form Helium with the liberation of energy.

The Process of fusion in the Sun starts off with two protons fusing to form a deuterium nuclide, a positron and a neutrino.

  $H+H\to H+e+{\nu }_e$

This reaction occurs twice in the process. The deuterium nuclide fuses with a proton to form a Helium-3 nuclide with the liberation of energy.

  $H+H\to He+\gamma$

This reaction occurs twice producing 2 nuclides of Helium -3 which then fuse to give a Helium -4 nuclide and liberating 2 protons.

  $He+He\to He+2H+\gamma$

The overall reaction can be written as,

  $\begin{array}{l}2H+2H\to \bcancel{2H}+2e+2{\nu }_e\\ \bcancel{2H}+\bcancel{2H}\to \bcancel{2He}+\gamma \\ \bcancel{He}+\bcancel{He}\to He+\bcancel{2H}+\gamma \\ \boxed{4H\to He+2e+2{\nu }_e+E}\end{array}$

This fusion generates energy since the mass of 4 protons is found to be greater than the product Helium nuclide. According to Einstein's equation for mass-energy equivalence, $E=\Delta m{c}^2$ the mass defect $\Delta m$ is converted into energy.

Conclusion:

Thus, at the center of the Sun, fusion converts hydrogen into helium and energy. The correct option is (c).