Transcript Topic 13_2__Nuclear physics

Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
13.2.1 Explain how the radii of nuclei may be
estimated from charges particle scattering
experiments.
13.2.2 Describe how the masses of nuclei may be
determined using a Bainbridge mass
spectrometer.
13.2.3 Describe one piece of evidence for the
existence of nuclear energy level.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Explain how the radii of nuclei may be estimated
from charged particle scattering experiments.
As you may recall from Topic 7, Rutherford
determined that the bulk of the atom’s positive
charge (and mass) is located in a very small
central nucleus have a radius of about 10-15 m.
If we analyze a head-on collision between an
alpha particle and a nucleus, we can obtain a
rough value for the diameter of a nucleus.
A nucleus has a charge of positive Ze and an
alpha particle has a charge of positive 2e.
As the alpha particle approaches the nucleus it
will be slowed down, stopped (for an instant),
and reversed by the Coulomb force.
FYI
Review Topic 7 for much of what is in this
option.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Explain how the radii of nuclei may be estimated
from charged particle scattering experiments.
rmax
The alpha particle feels a coulomb potential
caused by the nucleus given by V = kQ/r or
V = kZe/r.
If the alpha particle approaches from infinity,
the work needed to stop it at rmax is given by
W = qV = 2eV = 2kZe2/rmax.
From the work-kinetic energy theorem (W = ∆EK) we
get W = EK-EK,0. Since at rmax, EK = 0, W = EK,0.
rmax = 2kZe2/EK,0
nuclear radius
where EK,0 is the initial kinetic energy of the 
particle.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Explain how the radii of nuclei may be estimated
from charged particle scattering experiments.
rmax = 2kZe2/EK,0
nuclear radius
EXAMPLE:
of EK = 5
straight
nucleus.
Alpha particles having a kinetic energy
MeV bombard a gold nucleus and rebound
back. Estimate the radius of the gold
Why is the actual radius of
rmax
the nucleus less than rmax.
SOLUTION: Gold (Au) has Z = 79.
The alpha particle’s kinetic energy must be
converted to joules:
EK,0 = (5106 eV)(1.610-19 J/eV) = 810-13 J.
Then rmax = 2kZe2/EK,0
= 2(9109)(79)(1.610-19)2/810-13
= 510-14 m.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Describe how the masses of nuclei may be
determined using a Bainbridge mass spectrometer.
Recall the mass spectrometer in which an atom is
stripped of its electrons and accelerated
through a voltage into
a magnetic field.
Scientists determined
through the use of such
a device that hydrogen
nuclei came in three
different masses:
Since the charge of
the hydrogen nucleus is e, scientists
postulated the
existence of a neutral
particle called
the neutron.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Describe how the masses of nuclei may be
determined using a Bainbridge mass spectrometer.
While in the magnetic field the charged particle
feels a centripetal
force caused by the
magnetic field of
Fc = qvB sin .
But the angle between
v and B is 90° so that
sin  = 1.
Since Fc = mv2/r then
mv2/r = qvB so that
r = mv/(qB) mass and
radius
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Describe how the masses of nuclei may be
determined using a Bainbridge mass spectrometer.
PRACTICE:
B-field Source
Track X shows the deflection of a
singly-charged carbon-12 ion in the
deflection chamber of a mass
A
spectrometer. Which path best shows
B
the deflection of a singly-charged
X
carbon-14 ion? Assume both ions
C
travel at the same speed.
SOLUTION:
D
Since carbon-14 is heavier, it will
have a bigger radius than carbon-12.
Since its mass is NOT twice the mass of carbon12, it will NOT have twice the radius.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Describe how the masses of nuclei may be
determined using a Bainbridge mass spectrometer.
EXAMPLE: A hydrogen ion (proton) is accelerated
through a potential difference of V = 475 V and
projected into a mass spectrometer having a
magnetic field strength of 0.250 T.
(a) What is the velocity of the proton after its
acceleration?
(b) What is its radius of curvature in the spec?
SOLUTION:
(a) EK = qV = (1.610-19)(475) = 7.610-17 J.
Then 7.610-17 = (1/2)mv2 = (1/2)(1.6710-27)v2 and
v = 3.0105 ms-1.
(b) r = mv/(qB)
= (1.6710-27)(3.0105)/[(1.610-19)(0.250)]
= 0.013 m (1.3 cm)
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Describe one piece of evidence for the existence
of nuclear energy levels.
Recall that electrons in an atom moving from an
excited state to a de-excited state release a
photon.
Atomic spectral lines.
The emission spectra of
de-exciting atoms show
the existence of atomic energy levels.
In exactly the same way, de-exciting nuclei also
release photons which also produce spectra - only
with very high energy photons called gamma  rays:
234Pu*
234Pu

+

Nuclear spectral lines.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
13.2.4 Describe + decay, including the existence
of the neutrino.
13.2.5 State that the radioactive decay law is an
exponential function and define the decay
constant.
13.2.6 Derive the relationship between the decay
constant and the half-life.
13.2.7 Outline methods for measuring the halflife of an isotope.
13.2.8 Solve problems involving radioactive halflife.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Describe beta plus (+) decay including the
existence of the neutrino.
There are two types of beta () particle decay:
In - decay, a neutron
becomes a proton and an
electron is emitted from
the nucleus.
14C  14N +  + eIn + decay, a proton
becomes a neutron and a
positron is emitted from
the nucleus.
10C  10B +  + e+
In short, a beta particle is either an electron
or an anti-electron.
-
+
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Describe beta plus (+) decay including the
existence of the neutrino.
In contrast to the alpha particle, it was
discovered that beta particles could have a large
variety of kinetic energies.
Same
total
energy
In order to conserve energy it was postulated
that another particle called a neutrino was
created to carry the additional EK needed to
balance the energy.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive material
remaining
Radioactive decay
State the radioactive decay law as an exponential
function and define the decay constant.
The higher the initial population of a radioactive material, the more decays there
will be in a time interval.
But each decay decreases the
population.
Hence the decay rate
decreases over time for a
fixed sample and it is an
Time in half-lives
exponential decrease.
N = Noe-t
population decay
where N0 is the initial population, N is the new
one, t is the time, and  is the decay constant.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Derive the relationship between decay constant
and half-life.
EXAMPLE: Show that the relationship between halflife and decay constant is given by T1/2 = ln 2/.
SOLUTION: Use N = Noe-t. Then N = N0/2 when t = T1/2.
Exponential decay function.
Then
N = Noe-t
Substitution.
N0/2 = Noe-T
Cancel N0.
(1/2) = e-T
ln x and ex are inverses.
ln(1/2) = -T1/2
Multiply by -1.
-ln(1/2) = T1/2
-ln (1/x) = +ln x.
ln 2 = T1/2
T1/2 = ln 2/
decay constant and half-life
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Solve problems involving radioactive half-life.
EXAMPLE: The half-life of U-238 is 4.51010 y and
for I-123 is 13.3 h. Find the decay constant for
each radioactive nuclide.
SOLUTION:
Use T1/2 = ln 2/. Then  = ln 2/T1/2.
For U-238 we have
 = ln 2/T1/2 = 0.693/4.51010 y = 1.510-11 y-1.
For I-123 we have
 = ln 2/T1/2 = 0.693/13.3 h = 0.052 h-1.
FYI
The decay constant is the probability of decay
of a nucleus per unit time.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Outline methods for measuring the
isotope.
Rather than measuring the amount
radioactive nuclide there is in a
is hard to do) we measure instead
(which is much easier).
Decay rates are measured
using various devices, most
commonly the Geiger-Mueller
counter.
Decay rates are measured
in Becquerels (Bq).
1 Becquerel
1 Bq = 1 decay / second
half-life of an
of remaining
sample (which
the decay rate
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Outline methods for measuring the half-life of an
isotope.
The decay rate A is given by
A = -∆N/∆t = N = Noe-t
decay rate or activity
The ∆N is the change in the number of nuclei, and
is negative (the radioactive sample loses
population with each decay).
The negative sign is in A = -∆N/∆t to make the
activity A positive.
A = N shows that the activity is proportional to
the remaining population of radioactive nuclei,
which we learned in Topic 7.
Since N = Noe-t the last equation A = Noe-t is
true.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Solve problems involving radioactive half-life.
PRACTICE:
Remember that the mass of the material does not
change appreciatively during radioactive decay.
Nuclei are just transmuted.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Solve problems involving radioactive half-life.
PRACTICE:
0e
1
1p
1
It is a proton.
If you look at the lower numbers you see that we
are short a positive charge on the right:
The only two particles with a positive charge
(that we have studied) are the beta+ and the
proton.
Looking at the nucleon number we see that it
must be the proton.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Solve problems involving radioactive half-life.
PRACTICE:
The CO2 in the atmosphere has a specific
percentage of carbon-14.
The moment the wood dies, the carbon-14 is
NOT replenished.
Since the carbon-14 is always disintegrating
and is NOT being replenished in the dead wood,
its activity will decrease over time.
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Solve problems involving radioactive half-life.
PRACTICE:
From Thalf = ln 2/ we get  = ln 2/Thalf
or  = 0.693/5500 = 0.00013 y-1.
From A = N we see that in the beginning
9.6 = N0 and now 2.1 = N.
Thus N = N0e-t becomes 2.1 = 9.6e-t so that
2.1/9.6 = e-t.
ln(2.1/9.6) = ln(e-t)
-1.5198 = -t
t = 1.5198/0.00013 = 12000 y
Topic 13: Quantum and nuclear physics
13.2 Nuclear physics
Radioactive decay
Solve problems involving radioactive half-life.
PRACTICE:
The activity would be too small to be
reliable.
For this sample
A = 9.1e-t becomes
A = 9.1e-0.00013(20000) = 0.68 decay min-1.