Question

A portion of the Sun's energy comes from the reaction $$ 4 \mathrm{l} \mathrm{H} \cdots{ }_{2}^{4} \mathrm{He}+2 \mathrm{le} $$ This reaction requires a temperature of about \(10^{6}\) to \(10^{7} \mathrm{~K}\). (a) Why is such a high temperature required? (b) Is the Sun solid?

Short answer

(a) The high temperature is required for the reaction because it provides the necessary kinetic energy to the hydrogen nuclei to overcome the electrostatic repulsion and bring them close enough for the nuclear forces to bind them together, resulting in the formation of helium nuclei and energy release. (b) The Sun is not a solid; it is primarily composed of plasma due to the high temperatures required for nuclear reactions to occur.

Step-by-step solution

Understand the Nuclear Reaction

The given nuclear reaction shows that four hydrogen (H) nuclei combine to form a helium (He) nucleus and two electrons (e). This is a fusion reaction that takes place within the Sun, producing energy in the form of light and heat.

Reason for High Temperature Requirement

The high temperature is required for this reaction because, at such temperatures, the hydrogen nuclei (protons) have enough kinetic energy to overcome their repulsive electrostatic forces (due to their positive charges), and get close enough for the attractive strong nuclear force to come into play and bind them together. So, at high temperatures, the hydrogen nuclei move faster, increasing the chances of successful collisions and the formation of helium nuclei, which will release energy. Therefore, the given reaction requires temperatures in the range of \(10^6\) to \(10^7\) K. (a) The high temperature is required for the reaction because it provides the necessary kinetic energy to the hydrogen nuclei to overcome the electrostatic repulsion and bring them close enough for the nuclear forces to bind them together, resulting in the formation of helium nuclei and energy release.

Determine if the Sun is Solid

Based on the given information, we know that the Sun's energy comes from nuclear reactions occurring inside it. These reactions require extremely high temperatures. At such temperatures, atoms are separated into ions and electrons, forming a state of matter called plasma. Therefore, the Sun is primarily composed of plasma and not a solid. (b) The Sun is not a solid; it is primarily composed of plasma due to the high temperatures required for nuclear reactions to occur.

Key concepts

Nuclear Reaction

A nuclear reaction is a process in which the nucleus of an atom undergoes a transformation. In the core of the Sun, this transformation involves the fusion of hydrogen atoms to form helium. Such reactions underpin the immense energy the Sun produces, manifesting as both light and heat.

During the fusion process, hydrogen nuclei, which are simply protons, fuse together to form a helium nucleus. This process is illustrated by the equation: \[\begin{equation}4 \text{1H} \rightarrow \text{2}^4\text{He} + 2 \text{e}^-\text{H} \end{equation}\]Here, four protons (\text{1H}) come together to produce a helium nucleus (\text{2}^4\text{He}) and two electrons (\text{e}^-). It's important to underscore the fact that nuclear reactions, such as the one that powers the Sun, can release a substantial amount of energy. The conversion of mass to energy in this reaction is governed by Einstein's famous equation, E=mc^2, which indicates that even a tiny amount of mass can be converted into a significant amount of energy.

In this transformative reaction, nuclear forces outweigh the usually dominant electrostatic forces, which ordinarily repel protons from each other due to their like charges. Achieving this requires specific conditions which are naturally found in the Sun's core.

Electrostatic Forces

Electrostatic forces are the forces between charged particles. In simple terms, like charges repel each other and opposite charges attract each other. These forces are a key player in nuclear reactions, particularly in the Sun, where positively charged hydrogen nuclei repel each other due to their like positive charges.

Given that electrostatic forces are inherently repulsive between same-charged particles, the high temperature within the Sun's core becomes crucial. At the intense temperatures of approximately 10 million degrees Kelvin, hydrogen nuclei gain sufficient kinetic energy that allows them to move fast enough to overcome this repulsion and get close enough for nuclear fusion to occur. It's this overcoming of electrostatic forces that initiates the fusion process, binding protons together despite their natural tendency to repel due to these forces.

Overcoming Repulsion

For fusion to occur in the Sun, the nuclei must collide with enough energy to overcome the electrostatic repulsive force. This scenario can be imagined much like two magnets with the same pole facing each other; without enough force to push them together, they will not touch. Similarly, in the Sun's core, it's the intense kinetic energy provided by the extreme temperatures that allows protons to collide and stick together, defying their electrostatic repulsion.

Plasma State of Matter

The plasma state of matter is often referred to as the fourth state of matter, distinct from the solid, liquid, and gaseous states. In a plasma, atoms are energized to the point that electrons are freed from their nuclei, creating a hot, ionized gas consisting of free electrons and ions.

In the context of the Sun, the extreme temperatures lead to the formation of plasma. This high-energy state allows charged particles to be in constant, frenetic motion, and the sheer energy within the plasma facilitates the conditions necessary for nuclear fusion to occur. Unlike solids, where atoms are closely packed and maintain their shape, plasma does not have a fixed shape or volume and is rarely found naturally on Earth. However, it is the most common state of matter in the universe, as seen in stars, including our Sun.

Properties of Plasma

Plasma is highly conductive and responds strongly to electromagnetic fields, which further contributes to the dynamic behavior of the Sun's material. It's these properties of plasma, combined with the energetic environment found within a star, that allow nuclear reactions to be sustained, powering stars throughout their lifespans.