The atomic masses of nitrogen-14. titanium-48 and xenon-129 are 13.999234 amu. 4
ID: 832444 • Letter: T
Question
The atomic masses of nitrogen-14. titanium-48 and xenon-129 are 13.999234 amu. 47.935878 amu. and 128.904779 amu. respectively For 48Ti. calculate the nuclear binding energy. Express your answer using six significant figures. For l29Xe. calculate the nuclear binding energy. Express your answer using seven significant figures. For 14N calculate the nuclear binding energy per nucleon Express your answer using six significant figures. For 48Ti. calculate the nuclear binding energy per nucleon. Express your answer using six significant figures. For 129Xe. calculate the nuclear binding energy per nucleon. Express your answer using seven significant figures.Explanation / Answer
Nuclear binding energy is the energy required to split a nucleus of an atom into its component parts: protons and neutrons, or, collectively, the nucleons.
The actual mass of a nucleus is always less than the sum of the individual masses of the constituent protons and neutrons because energy is removed when when the nucleus is formed. This difference between the actual mass of an atom's nucleus and its expected mass based on the sum of the masses of its non-bound components.is known as mass defect.
This mass defect, is the missing mass in the resulting nucleus and represents the energy released when the nucleus is formed.
Mass defect (Md) is calculated using the following formula
Md=(mn+mp)mo
where
mp = mass of its protons (1mp = 1.00728 amu)
mn = mass of its neutrons (1 mn = 1.00867 amu)
(mo) = observed atomic mass
Once mass defect is known, nuclear binding energy can be calculated by converting that mass to energy by using
E=mc2. Mass must be in units of kg.
This energy, which is a quantity of joules for one nucleus, is known, it can be scaled into per-nucleon and per-mole quantities. To convert to joules/mole, simply multiply by Avogadro's number. To convert to joules per nucleon, simply divide by the number of nucleons.
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For 48 Ti calculate the binding energy:
Number of protons = 22 (Calcualted mass of total number of protons: 22 x 1.00728 = 22.16016 amu)
Number of neutrons = 26 (Calcualted mass of total number of neutrons: 26 x 1.00867 = 26.22542 amu )
Calcualted total mass of number of protons and neutrons, mp = 22.16016 + 26.22542 amu
Calcualted total mass of number of protons and neutrons, mn = 48.38558 amu
observed atomic mass, mo = 47.935878
Since mass defect is,
Md = (mn+mp)mo
Md = 48.38558 - 47.935878
= 0.449702 amu
Convert amu into Kg units
= 0.449702 amu x 1.66054 x 10-27 kg/amu
= 0.74674816 x 10-27 kg
Now calculate the energy:
E = mc2
E = 0.74674816 x 10-27 kg x (2.99792458 x 108 m/s )2
= 0.74674816 x 10-27 kg x 8.98755179 x 1016
Binding energy of 48 Ti nucleus, E = 6.7114377 x 10-11 J/atom
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For 129 Xe calculate the binding energy:
Number of protons = 54 (Calcualted mass of total number of protons: 54 x 1.00728 = 54.39312 amu)
Number of neutrons = 77 (Calcualted mass of total number of neutrons: 77 x 1.00867 = 77.66759 amu )
Calcualted total mass of number of protons and neutrons, mp = 54.39312 + 77.66759 amu
Calcualted total mass of number of protons and neutrons, mn = 132.06071 amu
observed atomic mass, mo = 128.904779
Since mass defect, Md = (mn+mp)mo
= 132.06071 - 128.904779
= 3.155931 amu
Convert amu into Kg units (1 amu = 1.66054 x 10-27 kg/amu)
= 3.155931 amu x 1.66054 x 10-27 kg/amu
= 5.2405496 x 10-27 kg
Now calculate the energy:
E = mc2
E = 5.2405496 x 10-27 kg x (2.99792458 x 108 m/s )2
= 5.2405496 x 10-27 kg x 8.98755179 x 1016
Binding energy of 129 Xe nucleus, E = 47.0997109 x 10-11 J
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For 14 N calculate the binding energy per nucleon:
Number of protons = 7 (Calcualted mass of total number of protons: 7 x 1.00728 = 7.05096 amu)
Number of neutrons = 7 (Calcualted mass of total number of neutrons: 7 x 1.00867 = 7.06069 amu )
Calcualted total mass of number of protons and neutrons, mp = 7.05096 + 7.06069 amu
Calcualted total mass of number of protons and neutrons, mn = 14.11165 amu
observed atomic mass, mo = 13.999234
Since mass defect, Md = (mn+mp)mo
= 14.11165 - 13.999234
= 0.112416 amu
Convert amu into Kg units (1 amu = 1.66054 x 10-27 kg/amu)
= 0.112416 amu x 1.66054 x 10-27 kg/amu
= 0.1866712 x 10-27 kg
Now calculate the energy:
E = mc2
E = 0.1866712 x 10-27 kg x (2.99792458 x 108 m/s )2
= 0.1866712 x 10-27 kg x 8.98755179 x 1016
E = 1.677717 x 10-11 J/ 14N atom
Number of nucleons = 14
Binding energy per nucleon of 14N atom = 1.677717 x 10-11/14 = 0.1198369 x 10-11 J/nucleon
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For 48 Ti calculate the binding energy per nucleon:
binding energy of 48 Ti, E = 6.7114377 x 10-11 J/atom
Number of nucleons = 48
Binding energy of per nucleon of 48 Ti atom = 6.7114377 x 10-11 J/atom / 48
Binding energy of per nucleon of 48 Ti atom = 0.1398216 x 10-11 J/nucleon
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For 129 Xe calculate the binding energy per nucleon:
the binding energy of 129 Xe atom, E = 47.0997109 x 10-11 J/atom
Number of nucleons = 131
Binding energy per nucleon of 129 Xe atom = 47.0997109 x 10-11 J/atom / 131
Binding energy per nucleon of 129 Xe atom = 0.3595397 x 10-11 J/nucleon
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