a. Calculate the mass defect in Fe-56 if the mass ofan Fe-56 nucleus is 55.921 amu. The...
a. Calculate the mass defect in Fe-56 if the mass of an Fe-56 nucleus is 55.921 amu. The mass of a proton is 1.00728 amu and the mass of a neutron is 1.008665 amu.
b. Determine the binding energy of an O-16 nucleus. The O-16 nucleus has a mass of 15.9905 amu. A proton has a mass of 1.00728 amu, a neutron has a mass of 1.008665 amu, and 1 amu is equivalent to 931 MeV of energy.
c. What percentage of a radioactive substance remains after 7.00 half-lives have elapsed?
d. Carbon-11 is used in medical imaging. The half- life of this radioisotope is 20.4 min. What percentage of a sample remains after 60.0 min?
Solutions
Expert Solution
Concepts and reason
The concepts used to solve the given questions are based on the mass defect, binding energy and percentage of the remaining amount.
Firstly, mass defect in Fe−56 is calculated. Secondly, the binding energy of O−16 is determined and then the percentage of remaining amount is calculated using the given half-lives of the respective sample.
Fundamentals
Mass defect:
It is the difference between the mass of an isotope and its mass number. The unit of mass defect is (amu).
1amu=931MeV
The formula of the mass defect (Δm) as shown below.
Δm=[Z(mp)+(A−Z)mn]−matom …… (1)
Here, Z is the atomic number, A is the mass number, mp is the mass of a proton, mn is the mass of the neutron.
Binding energy:
This is energy which binds the nucleus together. It is equal to the mass defect.
B.E=Δm …… (2)
The number of half-lives can be calculated as follows.
n=halflifeTimeelapsed …… (3)
Percentage of the remaining amount can be calculated as follows.
(%)=2n1×100 …… (4)
Here, n is the number of half-lives.
(12.a)
To calculate the mass defect in Fe−56 , substitute the value of Z as 26 , A as 56 , mp as 1.00728amu , mn as 1.008665amu and matom as 55.921amu in the equation (1).
To calculate the mass defect in O−16 , substitute the value of Z as 8 , A as 16 , mp as 1.00728amu , mn as 1.008665amu and matom as 15.9905amu in the equation (1).
A) Calculate the mass defect of the helium nucleus 52He. The
mass of neutral 52He is given by MHe=5.012225amu. Answer
in amu
B) Calculate the binding energy E of the helium nucleus
52He (1eV=1.602×10−19J). Answer in Mev
C) Calculate the binding energy per nucleon of the helium
nucleus 52He. Answer in MeV
Calculate the mass defect of the boron nucleus 11 5B. The mass
of neutral 11 5B is equal to 11.009305 atomic mass units. Express
your answer in atomic mass units to four significant figures.
Part B
Calculate the binding energy E of the boron nucleus 11 5B
(1eV=1.602×10−19J). Express your answer in millions of electron
volts to four significant figures.
Part C
Calculate the binding energy per nucleon of the boron nucleus 11
5B. Express your answer in millions of...
A)
Calculate the mass defect of the oxygen nucleus
16 8O. The mass of neutral 16 8O is equal to
15.994914 atomic mass units.
Express your answer in atomic mass units to four significant
figures.
B)
Calculate the binding energy E of the oxygen nucleus
16 8O (1eV=1.602×10−19J).
Express your answer in millions of electron volts to four
significant figures.
C)
Calculate the binding energy per nucleon of the oxygen
nucleus 16 8O.
Express your answer in millions of electron volts to four
significant...
A) Calculate the mass defect of the oxygen nucleus
16 8O. The mass of neutral 16 8O is equal to
15.994914 atomic mass units. Answer in amu.
B) Calculate the binding energy E of the oxygen nucleus
16 8O (1eV=1.602×10−19J). Answer in MeV
C) Calculate the binding energy per nucleon of the
oxygen nucleus 16 8O. Answer in MeV / nucleon
Nuclear Binding Energy
a)Calculate the mass defect of the helium nucleus 52He. The mass
of neutral 52He is given by MHe=5.012225amu. Express your answer in
atomic mass units to four significant figures.
b)Calculate the binding energy E of the helium nucleus 52He
(1eV=1.602×10−19J). Express your answer in millions of electron
volts to four significant figures.
c)Calculate the binding energy per nucleon of the helium nucleus
52He. Express your answer in millions of electron volts to four
significant figures.
Nuclear binding energy
Part D
Calculate the mass defect of the helium nucleus 52He. The mass
of neutral 52He is given by MHe=5.012225amu.
Express your answer in atomic mass units to four significant
figures.
amu
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Part
Part E
Calculate the binding energy E of the helium nucleus
52He (1eV=1.602×10−19J).
Express your answer in millions of electron volts to four
significant figures.
E =
MeV
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Part
Part F
Calculate the binding energy per nucleon of...
V-51 (atomic mass = 50.94396 amu)
Mass defect? Amu
Binding energy per nucleon? express answer using four sig figs.
Me/V nucleon
Ag-107 (atomic mass = 106.905092 amu)
Express your answer using five decimal places.
Mass defect? amu
Binding energy per nucleon? Me/V nucleon
four sig figs.
A Fe-56 atom (iron-56) contains 26 protons in its nucleus.
Determine the number of neutrons in its nucleus and then calculate
the nuclear binding energy per nucleon for Fe-56. The atomic mass
of Fe-56 is 55.934939 u.
492 MeV
18.9 MeV
8.79 MeV
16.4 MeV
9.14 MeV
A metal, M, of atomic mass 56 amu reacts with chlorine to form a
salt that can be represented as MClx. A boiling point elevation
experiment is performed to determine the subscript x, and
therefore, the formula of the salt. A 29.2 g sample of the salt is
dissolved in 100.0 g of water and the boiling point of the solution
is found to be 377 K. Find the formula of the salt. Assume complete
dissociation of the salt in...
The proton mass is 1.007276 amu , the neutron mass is 1.008665
amu , and the electron mass is 5.486×10−4 amu .
What is the expected mass of a potassium-39 nucleus, based on
the total mass of its protons and neutrons?
The actual measured mass of a potassium-39 atom is 38.963707 amu
. What is the mass defect, Δm, for a potassium-39
nucleus?
What is the binding energy for a potassium-39 nucleus?
What is the binding energy, ΔE, for a...