1) Suppose we start with a 1.00 g sample of a radioactive element. After 4.00 ye
ID: 867079 • Letter: 1
Question
1) Suppose we start with a 1.00 g sample of a radioactive element. After 4.00 years, 0.908 g remains. What is the half-life of this element in years?
4.05
3.63
28.80
41.60
4.40
2) Calculate the nuclear binding energy per nucleon for lithium-7 if the exact mass of this atom is 7.016004 amu? The exact mass of a proton is 1.007276467 amu and the exact mass of a neutron is 1.008664916 amu. Answer must be within 1% of the actual answer so carry at least 6 significant digits. Give all the answers in pico-J per nucleon. Remember that the "pico-" prefex means 10E-12.
Explanation / Answer
1)
[A] = [A0] (1/2) ^(t/hl)
0.908 = 1 (0.5) ^(4 / hl)
solve for Hl or halflife
0.908 = 0.5 ^(4/hl)
hl = 28.8 years
2)
Li-7 is made of 3 protons and 4 neutrons (and 3 electrons if neutral).
Therefore, the mass of 3 protons by themselves should be
3 * 1.007276467 = 3.021829401
The mass of 4 neutrons by themselves should be
4 * 1.008664916 = 4.034659664
The sum of the individual hadrons = 3.021829401+4.034659664 = 7.056489065 amu
The difference is around 0.0405 amu = 37.7 MeV (using 931.494 MeV per amu)
1 MeV = 1.60217657
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