College Physics
College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 30, Problem 33P
To determine

Number of electrons and quark particle in 1.00L .

Expert Solution & Answer
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Answer to Problem 33P

There are 3.34×1026 electrons, 9.36×1026 up quarks and 8.70×1026 down quarks.

Explanation of Solution

Given info:

Mass of water is 1.00L .

Avogadro number is 6.02×1023molecules/mol .

The number of gram per mole of water is 18.0g/mol .

Formula to the total number of molecules in water is,

N=mnNA

  •   N is the number of molecules
  • m is the mass of water
  • n is the number of gram per mole of water
  • NA is the Avogadro number

Substitute 1.00L for m , 6.02×1023molecules/mol for NA and 18.0g/mol for n to find N .

N=(1.00L)(1000g1L)(18.0g/mol)(6.02×1023molecules/mol)=3.34×1025molecules

Each molecule contains 10 protons, 10 electrons, and 8 neutrons.

Formula to the total number of electron in 1.00L of water is,

Ne=neN

  •   N is the number of molecules
  • ne is the number of electron in one molecule of water
  • Ne is the total number of electron in 1.00L of water

Substitute 3.34×1025molecules for N and 10electrons/molecule for ne to find Ne .

Ne=(10electrons/molecule)(3.34×1025molecules)=3.34×1026electrons

Thus, the total number of electrons in 1.00L of water is 3.34×1026electrons .

Formula to the total number of proton in 1.00L of water is,

Np=npN

  • np is the number of proton in one molecule of water
  • Np is the total number of proton in 1.00L of water

Substitute 3.34×1025molecules for N and 10protons/molecule for np to find Np .

Np=(10protons/molecule)(3.34×1025molecules)=3.34×1026protons

Thus, the total number of protons in 1.00L of water is 3.34×1026protons .

Formula to the total number of neutron in 1.00L of water is,

Nn=nnN

  • nn is the number of neutron in one molecule of water
  • Nn is the total number of neutron in 1.00L of water

Substitute 3.34×1025molecules for N and 8neutron/molecule for nn to find Nn .

Nn=(8neutron/molecule)(3.34×1025molecules)=2.68×1026protons

Each proton contains 2 up quarks and 1 down quark. Each neutron contains 1 up quark and 2 down quarks.

Formula to the total number of up quarks in 1.00L of water is,

Nu=2Np+Nn

  •   Nu is the total number of up quarks

Substitute 3.34×1026protons for Np and 2.26×1026neutrons for Nn to find Nu .

Nu=2(3.34×1026protons)+(2.26×1026neutrons)=9.36×1026up quarks

Formula to the total number of down quarks in 1.00L of water is,

Nd=Np+2Nn

  •   Nd is the total number of down quarks

Substitute 3.34×1026protons for Np and 2.26×1026neutrons for Nn to find Nd .

Nd=(3.34×1026protons)+2(2.26×1026neutrons)=8.70×1026up quarks

Thus, the total number of electrons in 1.00L of water is 3.34×1026electrons .

Conclusion:

There are 3.34×1026 electrons, 9.36×1026 up quarks and 8.70×1026 down quarks.

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