1. The mass of a proton is 1.00728 amu and that of a neutron is 1.00867 amu. Wha
ID: 1039879 • Letter: 1
Question
1. The mass of a proton is 1.00728 amu and that of a neutron is 1.00867 amu. What is the binding energy (in J) of a 60/27Co nucleus? (The mass of a cobalt-60 nucleus is 59.9338 amu. Speed of light = 3.00 × 108 m/s.)
a. 2.74 × 10^-19
b. 2.74 x 10^-16
c. 8.20 x 10^-11
d. 9.12 x 10^-28
e. 4.94 x 10^-13
2. What percentage of a radioactive sample remains after 175.0 yr if it has a half-life of 28.8 years?
a. 6.08
b. 84.8
c. 1.48
d. 0.230
e. 16.5
3. The half-life of carbon-11 is 20.3 minutes. How much of a 100.0 mg sample remains after 1.6 hours?
a. 99.9 mg
b. 1.75 x 10^-89 mg
c. 94.7 mg
d. 0.0377 mg
4. The half-life of cobalt-60 is 5.20 yr. How many milligrams of a 2.000-mg sample remain after 9.50 years?
a. 7.076
b. 0.565
c. 1.435
d. 7.03 x 10^-22
e. 1.095
e. 3.77 mg
Explanation / Answer
1.
binding energy(E) = DmC^2
Dm = mass defect
mass of proton = 1.00728 amu
mass of neutron = 1.00867 amu
Expected mass of Co = (27*1.00728+33*1.00867) = 60.5 amu
Actual mass of Co = 60 amu
Dm = Expected mass of Ba - Actual mass of Ba
= 60.5-60
= 0.5 amu
= 0.5/(6.022*10^26) kg (1 amu = 1/6.022*10^26 kg)
= 8.3*10^-28 kg
E = DmC^2
= (8.3*10^-28)*(3*10^8)^2
= 7.47*10^-11 joule
answer: C
2.
first order kinetics
K1 = 0.693/t1/2
= 0.693/28.8
= 0.024 days-1
k1 = (1/t)ln(a0/a)
a0 = initial concentration = 100
a = concentration remains after 175 years = x
t = time = 175 years
0.024 = (1/175)ln(100/x)
x = 1.48%
answer: C
3. K1 = 0.693/t1/2
= 0.693/20.3
= 0.034 min-1
k1 = (1/t)ln(a0/a)
a0 = initial concentration = 100
a = concentration remains after 1.6 hrs = x
t = time = 1.6*60 = 96 min
0.034 = (1/96)ln(100/x)
x = 3.82 mg
no answer available
4. K1 = 0.693/t1/2
= 0.693/5.2
= 0.133 y-1
k1 = (1/t)ln(a0/a)
a0 = initial concentration = 100
a = concentration remains after 9.5 years = x
t = time = 1.6*60 = 96 min
0.133 = (1/9.5)ln(2/x)
x = 0.565
answer: b.0.565 mg
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