12) a. Calculate the mass defect in Fe-56 if the mass of an Fe-56 nucleus is 55.
ID: 800719 • Letter: 1
Question
12) 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.
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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.
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c. What percentage of a radioactive substance
remains after 7.00 half-lives have elapsed?
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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?
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Explanation / Answer
12)
a)
mass defect = the calculated actual mass - the mass number of nucleus
no. of neutrons56 - 26 = 30
(26x1.00728) + (30x1.008665) - 55.921 = 0.528 amu
mass defect = 0.528 amu
b. An oxygen-16 has 8 protons and 8 neutrons. The sum of the masses
8*(1.00728 ) + 8*(1.0088665) = 16.12756 AMU.
mass defect = (16.12756 - 15.9905 )
BE = mass defect x 931 MeV
BE = (16.12756 - 15.9905)x931 MeV = 127.6 MeV
c.
Amount remaining after n t1/2 = 1 / 2^n
after 7 half-lives,
Amount remaining = 1 / 2^7 = 0.0078 %
d. Amount remaining = Initial amount / 2^n
where n= time elapsed/halflife
n= 60/20.4 = 2.941
Amount remaining = 100/2^2.941 = 100/7.679 = 13.023%
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