quantum and nuclear physics (b)
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Quantum and Nuclear Physics (B)
Problem Solving
Mr. KlapholzShaker Heights
High School
Problem 1An alpha particle is shot directly at a gold atom with a kinetic energy of 7.7 MeV. How close can the alpha get to the center of the nucleus?
Solution 1Electron-Volts is not an SI unit, so let’s convert:
7.7 x 106 eV ( 1.602 x 10-19 J / 1 eV ) = 1.2 x 10-12 J
Initial Ek of a = Electrical Ep at closest approach
1.2 X 10-12 = kQaQgold / R2
1.2 X 10-12 = [9.0x109] × [1.6 x 10-19] × [(79)(1.6x10-19)] / R2
R = ?R = 3.0 x 10-14 m
(Memorize size of nucleus ≈ 10-15 m)
Problem 2A sample of a radioactive isotope contains 1.0 x 1024 atoms and it has a half life of 6 hours. Find:a)The decay constant.b)The initial activity.c)The number of original nuclei still present after 12 hours.d)The number of original nuclei still present after 30 minutes.
Solution 2
a) We know that T½ = 6.0 hours. How do we find the decay constant?
ln(2) / l = T½
We will need S.I. units. T½ = ?
T½ = ( 6 hours )(3600 s / hour) = 21600 s
l = ln(2) / T½ = ln(2) / (21600 s)
l = 3.2 x 10-5 s-1 This is the probability that any single nucleus
will decay, in one second.
Solution 2
b) The “initial activity” is the original number of nuclei that decay per second.
A = lNA0 = lN0
A0 = [ 3.2 x 10-5 s-1 ] [ 1.0 x 1024 ]A0 = 3.2 x 1019 nuclei per second
A0 = 3.2 x 1019 Becquerel
A0 = 3.2 x 1019 Bq
Solution 2
c) 12 hours is 2 half lives.So, the number of original nuclei remaining is
one-fourth of the original.
N = ¼ × [ 1.0 x 1024 ] N = 2.5 x 1023 nuclei
Solution 2
d) Convert 30 minutes to SI units:( 30 minutes )( 60 s / minute ) = 1800 sThe number of nuclei that are still not
disintegrated is:N = N0e-lt
N = (1.0 x 1024)e-(3.2 x 10-5)(1800) = ?
N = 9.4 x 1023 nucleiCheck: this is more than N after 12 hours, and
less than N0.
Problem 3The background radiation rate is 10 counts per second. Find the half life.
Time / s Counts per second
0 210
1 110
2 60
3 35
Solution 3If you subtract the background rate, you’ll see that the half life is one second.
Time / s Counts per second MINUS background
0 200
1 100
2 50
3 25
Tonight’s HW:
Go through the Quantum and Nuclear section in your textbook and scrutinize the “Example Questions” and solutions.Bring in your questions to tomorrow’s
class.
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