/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 Which of these groups of particl... [FREE SOLUTION] | 91Ó°ÊÓ

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Which of these groups of particles has the greatest mass? (a) a helium nucleus with two protons and two neutrons (b) four electrons (c) four individual protons

Short Answer

Expert verified
(a) and (c) have the greatest mass, both equal at 6.68 × 10^{-27} kg.

Step by step solution

01

Determine mass of particles in option (a)

A helium nucleus consists of two protons and two neutrons. The mass of one proton is approximately 1.67 × 10^{-27} kg, and the mass of one neutron is nearly the same, around 1.67 × 10^{-27} kg too. Therefore, the total mass of a helium nucleus is:\[2 imes 1.67 \times 10^{-27} \, \text{kg (protons)} + 2 imes 1.67 \times 10^{-27} \, \text{kg (neutrons)} = 6.68 \times 10^{-27} \, \text{kg}\]
02

Determine mass of particles in option (b)

An electron has a much smaller mass of about 9.11 × 10^{-31} kg. Therefore, the mass of four electrons is:\[4 \times 9.11 \times 10^{-31} \, \text{kg} = 3.64 \times 10^{-30} \, \text{kg}\]
03

Determine mass of particles in option (c)

A proton has a mass of approximately 1.67 × 10^{-27} kg. Therefore, the mass of four individual protons is:\[4 \times 1.67 \times 10^{-27} \, \text{kg} = 6.68 \times 10^{-27} \, \text{kg}\]
04

Compare all masses from the options

From previous calculations: - Option (a): 6.68 × 10^{-27} kg (helium nucleus) - Option (b): 3.64 × 10^{-30} kg (four electrons) - Option (c): 6.68 × 10^{-27} kg (four protons) Options (a) and (c) have identical masses, which are greater than option (b), as the electron's mass is much less than that of protons or neutrons.

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Key Concepts

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

helium nucleus
The helium nucleus is a fundamental concept in understanding atomic structure. It consists of two protons and two neutrons. This combination forms what is known as an alpha particle. - The helium nucleus is a key part of the second element on the periodic table, helium, which is a noble gas. - In terms of mass, the helium nucleus is heavier than groups consisting solely of electrons. The helium nucleus is stable and plays a crucial role in nuclear reactions like those inside the sun. During such reactions, helium nuclei can be formed from the fusion of hydrogen nuclei. This process releases a vast amount of energy, which helps sustain the sun's brightness and warmth.
proton
The proton is a positively charged particle found in the nucleus of atoms. It is one of the essential building blocks of matter and, along with neutrons, determines the identity of an element. - Each proton has a charge of +1 and contributes significantly to an atom's overall mass. - The mass of a proton is approximately 1.67 × 10^{-27} kg, similar to that of a neutron. In the context of the exercise, when you group four individual protons, their combined mass equals that of a helium nucleus. This demonstrates the significant weight protons contribute to an atom's nucleus.
electron
Electrons are negatively charged particles that orbit the nucleus of an atom. They have a much smaller mass compared to protons and neutrons. - Each electron has a charge of -1 and a mass of about 9.11 × 10^{-31} kg, making them lightweight. - Due to their negligible mass, electrons contribute very little to the overall mass of the atom. In the exercise, the total mass of four electrons is significantly less than the mass of a helium nucleus or four individual protons, highlighting their minimal impact on atomic mass despite being crucial for chemical reactions and bonding.
neutron
Neutrons are neutral particles residing in the nucleus of atoms, playing a vital role in the structure and stability of the nucleus. - Neutrons do not carry a charge, which allows them to act as a balancing force between the positively charged protons in the nucleus. - They have a mass close to that of protons, around 1.67 × 10^{-27} kg, contributing to the bulk of an atom's mass. In a helium nucleus, there are two neutrons. These neutrons, along with protons, ensure the nucleus remains stable by reducing the electrostatic repulsion between protons.
particle physics
Particle physics is the branch of physics that studies the fundamental particles of the universe and the forces through which they interact. It provides the foundation for understanding atoms, nuclei, and the particles that compose them. - It explores particles such as protons, neutrons, electrons, and their interactions at the smallest scales. - Provides insight into the composition and behavior of matter, essential for technological advances and scientific discovery. The concepts of proton, electron, neutron, and helium nucleus fall under the realm of particle physics. This field helps us appreciate the fundamental components of matter and their behavior, aiding in analyses like the exercise where mass comparison of different particle combinations is required.

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Most popular questions from this chapter

The Sun's Future. Roles: Scribe (takes notes on the group's activities \(),\) Proposer (proposes explanations to the group), Skeptic (points out weaknesses in proposed explanations \(),\) Moderator (leads group discussion and makes sure everyone contributes). Activity: Consider what you have learned about how the Sun came to shine steadily with energy from fusion in its core, then discuss the following questions: a. What will happen to the core temperature of the Sun after the core runs out of hydrogen for fusion? Will the temperature go up or down? b. If you think the temperature will go up, will it rise forever? What could eventually stop the temperature from rising? If you think the temperature will go down, will it decrease forever? What could eventually stop it from falling? experiment or a set of stellar observations that could test your hypothesis from part b.

The Lifetime of the Sun. The total mass of the Sun is about \(2 \times 10^{30}\) kilograms, of which about \(70 \%\) was hydrogen when the Sun formed. However, only about \(13 \%\) of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion. a. Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun. b. The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part a, calculate how long the Sun's initial supply of hydrogen can last. Give your answer in both seconds and years. c. Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?

Describe how a natural "solar thermostat" keeps the core fusion rate steady in the Sun.

Solar Observatories in Space. Visit NASA's website for the Sun-Earth connection and explore some of the current and planned space missions designed to observe the Sun. Choose one mission to study in greater depth, and write a one- to two-page report on the status and goals of the mission and what it has taught or will teach us about the Sun.

What is the overall nuclear fusion reaction in the \(\operatorname{Sun}\) ? Briefly describe the proton-proton chain.

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