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Chapter 14: Problem 34

The Sun has a radius equal to about 2.3 light-seconds. Explain why a gamma ray produced in the Sun's core does not emerge from the Sun's surface 2.3 seconds later.

Short Answer

Expert verified
Gamma rays take thousands to millions of years to reach the Sun’s surface due to the random walk process caused by constant interactions with particles.

Step by step solution

01

- Understanding Light Travel Time

Calculate the time it would take for light to travel straight from the center of the Sun to its surface. The Sun's radius is given as 2.3 light-seconds, so in an unobstructed path, light would take 2.3 seconds to travel this distance.
02

- Nature of Gamma Rays in the Sun

Gamma rays are high-energy photons produced in the Sun's core during nuclear fusion. They collide with particles, such as electrons and nuclei, in the Sun, resulting in repeated scattering and absorption processes.
03

- Random Walk Process

Due to the density of the Sun's interior, gamma rays do not travel in a straight line. Instead, they undergo a random walk, repeatedly scattering and changing direction, thus greatly extending their journey to the surface.
04

- Mean Free Path of Photons

The mean free path, which is the average distance a photon travels between scatterings, is extremely short inside the Sun's core. This significantly increases the time it takes for a gamma ray to reach the surface.
05

- Time Delay Calculation

Estimations suggest that a gamma ray can take thousands to millions of years to finally emerge from the Sun’s surface due to the random walk process, in stark contrast to the 2.3 seconds if it could move unobstructed.
06

- Energy and Wavelength Changes

By the time a gamma ray exits the Sun, it has lost a considerable amount of energy through numerous interactions and is observed as a lower-energy photon, such as visible light.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

light travel time
When we talk about light travel time, we refer to how long it takes for light to move from one point to another. In the context of the Sun, if light could travel directly from its core to its surface, it would take 2.3 seconds. This is based on the radius of the Sun being 2.3 light-seconds. In space, light typically travels in a straight line because there is very little to obstruct its path. However, the Sun's interior is much denser, making this direct path impossible for gamma rays produced there.
random walk process
In many areas of science, a random walk describes a path that consists of a series of random steps. Inside the Sun, gamma rays produced by nuclear fusion do not travel in straight lines. Instead, they move through a 'random walk process.' This means they constantly change direction each time they collide with particles within the Sun. These collisions cause the gamma rays to scatter, making their journey to the surface take far longer than if they traveled straight. Due to this random walk, gamma rays can take thousands to millions of years to finally reach the Sun's surface.
mean free path
The mean free path is the average distance a photon (in this case, a gamma ray) travels before colliding with another particle. In the Sun's core, the mean free path of a gamma ray is extremely short due to the dense environment. This means that gamma rays are constantly bumping into electrons and nuclei, causing repeated scatterings. Because the mean free path is so short, the gamma rays have to interact many, many times before they can exit the Sun. This is why the journey from the core to the surface takes so long.
nuclear fusion
Nuclear fusion is the process that powers the Sun. It occurs in the core where the temperature and pressure are incredibly high. Here, hydrogen nuclei combine to form helium, releasing energy in the form of gamma rays. These high-energy photons start their long journey from the core towards the surface. Along the way, they transfer their energy to other particles via collisions, gradually transforming into lower-energy forms like visible light.
photon scattering
Photon scattering is a crucial process inside the Sun. It refers to the interaction of photons (like gamma rays) with other particles, causing the photons to deflect in different directions. In the dense core of the Sun, photon scattering happens frequently, preventing gamma rays from traveling straightforwardly. Each scatter alters the direction and energy of the gamma ray, contributing to its lengthy and arduous journey to the surface. Over time, these interactions cause the gamma rays to lose energy, ultimately emerging as less energetic photons like visible light.

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Most popular questions from this chapter

Describe the solar corona. Under what circumstances can it be seen without special instruments?

The hydrogen bomb represents an effort to create a similar process to what takes place in the core of the Sun. The energy released by a 5-megaton hydrogen bomb is \(2 \times 10^{16} \mathrm{J}\) a. This textbook, \(21^{\text {th }}\) Century Astronomy, has a mass of about 1.6 kg. If all of its mass were converted into energy, how many 5 -megaton bombs would it take to equal that energy? b. How much mass did Earth lose each time a 5-megaton hydrogen bomb was exploded?

Sunspots, flares, prominences, and coronal mass ejections are all caused by a. magnetic activity on the Sun. b. electrical activity on the Sun. c. the interaction of the Sun's magnetic field and the interstellar medium. d. the interaction of the solar wind and Earth's magnetic field. e. the interaction of the solar wind and the Sun's magnetic field.

The solar neutrino problem pointed to a fundamental gap in our knowledge of a. nuclear fusion. b. neutrinos. c. hydrostatic equilibrium. d. magnetic fields.

Why are neutrinos so difficult to detect?
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