Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
9th Edition
ISBN: 9781305372337
Author: Raymond A. Serway | John W. Jewett
Publisher: Cengage Learning
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Chapter 23, Problem 1P

Find to three significant digits the charge and the mass of the following particles. Suggestion: Begin by looking up the mass of a neutral atom on the periodic table of the elements in Appendix C. (a) an ionized hydrogen atom, represented as H+ (b) a singly ionized sodium atom, Na+ (c) a chloride ion Cl (d) a doubly ionized calcium atom, Ca++ = Ca2+ (e) the center of an ammonia molecule, modeled as an N3− ion (f) quadruply ionized nitrogen atoms, N4+, found in plasma in a hot star (g) the nucleus of a nitrogen atom (h) the molecular ion H2O

(a)

Expert Solution
Check Mark
To determine

The charge and mass of ionized hydrogen atom up to three significant digits.

Answer to Problem 1P

The charge and mass of ionized hydrogen atom is +1.60×1019C and 1.67×1027kg .

Explanation of Solution

The ionized hydrogen atom is H+ . Hydrogen atom has the atomic number one that is equal to the number of electrons and protons that means hydrogen atom consists of one electron and one proton.

When the hydrogen atom is ionized by emission of electron or absorption of electron, in emission process the electron is removed from the atom and in absorption process electron is gained, Hydrogen always forms the positive ion.

The charge is calculated as,

Charge ofH+=+e1.60×1019C

The mass is calculated as,

Mass ofH+=Massofproton=1.67×1027Kg

Conclusion:

Therefore, the charge of ionized hydrogen atom is +1.6×1019C and mass 1.67×1027Kg

(b)

Expert Solution
Check Mark
To determine

The charge and mass of singly ionized sodium atom Na+ upto three significant digits.

Answer to Problem 1P

The charge and mass of singly ionized sodium atom Na+ is +1.6×1019C and 3.82×1026kg .

Explanation of Solution

A singly ionized sodium atom is Na+ . As the electronic configuration of sodium atom is 2,8,1 , there is one electron in the outermost shell so to become stable or achieve noble gas electronic configuration it has to lose one electron or gain seven electrons. Seven electrons cannot be gained due to energy considerations. So it will lose one electron by losing the electron the number of electrons decreases compare to the number of protons. Sodium atom always forms the positive ion.

The charge of an ionized atom is given by the number of electron is gained or lost by the neutral atom as the atom forms an ion by losing a electron so its charge is +e .

The charge of sodium ion is,

Na+=+e=+1.6×1019C

The mass of electron is negligible compared to mass of Hydrogen. Sodium atom has more mass than the hydrogen atom so the positive ion of sodium atom that is formed by the loss of an electron has negligibly mass that can be ignored.

Mass ofNa+mass ofNa+3.82×1026Kg

Conclusion:

Therefore, the charge of ionized sodium atom is +1.6×1019C and mass is 3.82×1026Kg

(c)

Expert Solution
Check Mark
To determine

The charge and mass of ionized chlorine atom Cl up to three significant digits.

Answer to Problem 1P

The charge and mass of ionized chlorine atom Cl is 1.6×1019C and 5.89×1026kg .

Explanation of Solution

A ionized Chlorine atom that is represented is Cl- . Chlorine atom has the atomic number 17 which is equal to the number of electrons and protons that means Chlorine atom consists of 17 electrons and 17 protons. Electrons are revolving in the orbit and proton is residing inside the nucleus

When the Chlorine atom is ionized by emission of electron as the electronic configuration of Chlorine atom is 2,8,7 , there are seven electrons in the outermost shell so to become stable or achieve noble gas electronic configuration it has to gain one electron or lose seven electrons. Seven electrons cannot lose due to energy considerations. So it will gain one electron by gaining the electron the number of electrons increases compare to the number of protons. Chlorine atom always forms the negative ion.

The charge of an ionized atom is given by the number of electron is gained or lost by the neutral atom as the atom forms an ion by losing a electron so its charge is e .

The charge of Chlorine ion is,

Cl=e1.60×1019C

The mass of electron is negligible compared to mass of Hydrogen. Chlorine atom has more mass than the hydrogen atom so the negative ion of chlorine atom which is formed by the gain of an electron has negligibly mass that can be ignored.

Mass ofClmass of Cl5.89×1026Kg 

Conclusion:

The charge of ionized Chlorine atom is 1.6×1019C and mass 5.89×1026Kg .

(d)

Expert Solution
Check Mark
To determine

The charge and mass of doubly ionized Calcium atom Ca++=Ca2+ up to three significant digits.

Answer to Problem 1P

The charge and mass of doubly ionized Calcium atom Ca++=Ca2+ is +3.20×1019C and 6.65×1026kg

Explanation of Solution

A doubly ionized Calcium atom is Ca++=Ca2+ . When the Calcium atom is ionized by emission of electron as the electronic configuration of sodium atom is 2,8,8,2 , there is two electron in the outermost shell so to become stable or achieve noble gas electronic configuration it has to lose two electron or gain six electrons. Six electrons cannot be gain due to energy considerations. so it will lose two electron by losing the electron the number of electrons decreases compare to the number of protons. Calcium atom always forms the positive ion.

The charge of an ionized atom is given by the number of electron is gained or lost by the neutral atom as the atom forms an ion by losing two electron so its charge is +2e .

The charge of Calcium ion is,

Ca2+=+2e=2(1.6×1019C)+3.20×1019C

The mass of electron is negligible compared to mass of H. Calcium atom has more mass than the hydrogen atom so the positive ion of Calcium atom that is formed by the loss of two electron has negligibly mass that can be ignored.

Mass ofCa2+mass ofCa6.65×1026Kg

Conclusion:

Therefore, the charge of ionized Chlorine atom is +3.20×1019C and mass is 6.66×1026Kg .

(e)

Expert Solution
Check Mark
To determine

The charge and mass of the centre of ammonia molecule N3 up to three significant digits.

Answer to Problem 1P

The charge and mass of the centre of ammonia molecule N3 is 4.80×1019C and 2.33×1026kg

Explanation of Solution

The centre of ammonia molecule is N3 . When the Nitrogen atom is ionized by emission of electron as the electronic configuration of sodium atom is 2,5 , there are five electrons in the outermost shell so to become stable or achieve noble gas electronic configuration it has to lose five electrons or gain three electrons. Five electrons cannot lose as the atom collapse due to the removal of the orbit. So it will gain two electrons by gaining the electron the number of electrons increases compare to the number of protons. Nitrogen atom always forms the negative ion.

The charge of an ionized atom is given by the number of electron is gained or lost by the neutral atom as the atom forms an ion by losing a electron so its charge is +2e .

The charge of Nitrogen ion is,

N3=3e=3(1.6×1019C)4.80×1019C

The mass of electron is negligible compared to mass of Hydrogen. Nitrogen atom has more mass than the hydrogen atom so the negative ion of centre of Ammonia molecule atom which is formed by the gain of three electron has negligibly mass that can be ignored.

Mass ofN3mass ofN2.33×1026Kg

Conclusion:

The charge of centre of Ammonia molecule is 4.80×1019C and mass 2.33×1026Kg .

(f)

Expert Solution
Check Mark
To determine

The charge and mass of the quadruple ionized Nitrogen N4+ up to three significant digits.

Answer to Problem 1P

The charge and mass of the quadruple ionized Nitrogen N4+ is +6.40×1019C and 2.33×1026Kg

Explanation of Solution

The quadruple ionized Nitrogen atoms found in plasma of hot star is N4+ .

When the Nitrogen atom is ionized by emission of electron as the electronic configuration of sodium atom is 2,5 , there is five electrons in the outermost shell so to become stable or achieve noble gas electronic configuration it has to lose four electrons. As the nucleus of nitrogen is very strong which works as a plasma in hot star so that property of plasma does tends to collapse the atom although it has lose four of its electrons.

The charge of an ionized atom is given by the number of electron is gained or lost by the neutral atom as the atom forms an ion by losing four electrons so its charge is +4e .

The charge of quadruple Nitrogen ion is,

N4+=+4e=4(1.6×1019C)+6.40×1019C

The mass of electron is negligible compared to mass of Hydrogen. Nitrogen atom has more mass than the hydrogen atom so the positive ion of centre of quadruple atom that is formed by the loss of four electrons has negligibly mass that can be ignored.

Mass ofN4+mass ofN2.33×1026Kg

Conclusion:

The charge and mass of the quadruple ionized Nitrogen N4+ is +6.40×1019C and mass 2.33×1026Kg .

(g)

Expert Solution
Check Mark
To determine

The charge and mass of the nucleus of nitrogen atom N7+ upto three significant digits.

Answer to Problem 1P

The charge and mass of the nucleus of nitrogen atom N7+ is +11.2×1019C and 2.99×1026kg .

Explanation of Solution

The nucleus of nitrogen ion is N7+ . When the Nitrogen atom is ionized by emission of electron as the electronic configuration of sodium atom is 2,5 , there are five electrons in the outermost shell so to become stable or achieve noble gas electronic configuration it has to lose seven electrons. As the nucleus of nitrogen is very strong which works as a plasma in hot star so that property of plasma does tends to collapse the atom although it has lose all its electrons.

The charge of an ionized atom is given by the number of electron is gained or lost by the neutral atom as the atom forms an ion by losing a electron so its charge is +7e .

The charge of nucleus of Nitrogen ion is;

N7+=+7e=7(1.6×1019C)+1.12×1018C

The mass of electron is negligible compared to mass of Hydrogen. Nitrogen atom has more mass than the hydrogen atom so the positive ion of centre of quadruple atom that is formed by the loss of seven electrons has negligibly mass that can be ignored.

Mass ofN7+mass ofN2.33×1026Kg

Conclusion:

The charge of quadruple is +1.12×1018C and mass 2.33×1026Kg .

(h)

Expert Solution
Check Mark
To determine

The charge and mass of the Molecular ion H2O up to three significant digits.

Answer to Problem 1P

The charge and mass of the Molecular ion H2O is 1.6×1019C and 2.99×1026kg .

Explanation of Solution

The molecular ion of water is H2O . The atomic mass of water is eighteen in that the oxygen atom is attached to the two hydrogen atom. Oxygen has the valency of two it can share two electrons to the hydrogen atom and for a molecule as a whole it gains one electron and become a negative ion.

The charge of molecule of H2O ion is,

H2O=e1.6×1019C

The mass of electron is negligible compared to mass of Hydrogen. Water molecule has  more mass than the hydrogen atom so the ionized water molecule that is formed by the gain of one electron has negligibly mass that can be ignored.

Mass ofH2Omass ofH2O2.99×1026Kg

Conclusion:

Therefore, the charge of Molecule of H2O is 1.6×1019C and mass 2.99×1026Kg .

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Chapter 23 Solutions

Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University

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