Two small aluminum spheres, each having mass 0.02500.02500.0250 kg, are separated by 80.080.080.0 cm. What fraction of all the electrons in each sphere does this represent?

Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 21: Electric Charge and Electric Field

문제 8c

21장, 문제 8c

Two small aluminum spheres, each having mass $0.0250$ kg, are separated by $80.0$ cm. What fraction of all the electrons in each sphere does this represent?

검증된 단계별 안내

First, determine the number of aluminum atoms in each sphere. Use the formula for the number of moles: $ n = \frac{m}{M} $, where $ m $ is the mass of the sphere (0.0250 kg) and $ M $ is the molar mass of aluminum (approximately 27 g/mol or 0.027 kg/mol).

Convert the mass of the sphere from kilograms to grams to match the units of the molar mass: $ m = 0.0250 \text{ kg} \times 1000 \text{ g/kg} = 25 \text{ g} $.

Calculate the number of moles of aluminum in each sphere: $ n = \frac{25 \text{ g}}{27 \text{ g/mol}} $.

Determine the number of atoms in each sphere using Avogadro's number $ N_A = 6.022 \times 10^{23} \text{ atoms/mol} $: $ N = n \times N_A $.

Since each aluminum atom has 13 electrons, calculate the total number of electrons in each sphere: $ N_e = N \times 13 $. This gives the total number of electrons in one sphere, and you can compare this to the number of electrons involved in the interaction to find the fraction.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

12m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Atomic Structure of Aluminum

Aluminum is an element with atomic number 13, meaning each atom has 13 protons and, typically, 13 electrons. Understanding the atomic structure is crucial for calculating the total number of electrons in a given mass of aluminum, as it allows us to determine the number of atoms present.

Avogadro's Number

Avogadro's Number, approximately 6.022 x 10^23, is the number of atoms or molecules in one mole of a substance. This concept is essential for converting the mass of aluminum spheres into moles, which then allows us to calculate the total number of electrons by multiplying the number of moles by Avogadro's Number and the number of electrons per atom.

Fraction Calculation

To find the fraction of electrons involved, one must compare the number of electrons in the interaction to the total number of electrons in the spheres. This involves calculating the total number of electrons using atomic and molecular data, and then determining what portion of these electrons are relevant to the problem at hand.