1 Aside on the neutrinos Alpha decay and Tunneling Nuclear Reaction Kinematics Nuclear Spin Radioactive Decay Xray spectrum for Ru 106 Why is this isotope in the news not Cs 137 ID: 914118
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Slide1
Nuclear Physics Part III
1
Aside on the neutrinos
Alpha decay and TunnelingNuclear Reaction KinematicsNuclear SpinRadioactive Decay
X-ray spectrum for Ru106 -Why is this isotope in the news ? (not Cs137)
Ans: a plume of Ru106 has been detected all over Europe. Most likely from a Russian medical isotope facility. Dose is small.
Slide2Probability of ruthenium emission point using all measurements in Europe and weather info.
Technical analysis by French Nuclear Institute IRSN. [Ru
- signals reported by 43 nations.]
Question: What are medical isotopes used for ?Ans: Diagnosis and treatmentSee discussion on p.1461 of the text e.g. Technetium-99
Slide3An Aside: mass of the neutrino?
N
ote
the values of the masses: mp =1.007276 u, mn = 1.008665 u the proton is a stable particle. [Q: What is u ?]
3
Does the neutrino have mass?
SuperKamiokande
Water Tank in Gifu-ken (2015 Nobel Prize for
Kajita
)
There are mass differences between different types of nu’s
Slide4Review: Alpha decay
An
alpha particle α
is a 4He nucleus (2 protons and 2 neutrons) The α decay of the 226Ra (radium) nuclide to Radon.N.B. alpha decay requires quantum mechanical tunneling (original nucleus is bound and inside a potential well)
4
Slide5QM Tunneling and alpha decay
http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/alpdet.html#c1
Let’s work out a numerical example and remember how to calculate tunneling probabilities
5
Slide6QM Tunneling and alpha decay (I)
In a simple model for a radioactive nucleus, an alpha particle (m=6.64 x 10-27kg) is trapped by a square barrier that has width 2.0 fm and height 30 MeV.
What is the tunneling probability if the kinetic energy of the alpha particle is 1.0 MeV below the top of the barrier ? [Also try 10 MeV below U
0]E1 MeV
6
Slide7Example of QM Tunneling and alpha decay (II)
An alpha particle (m=6.64 x 10-27kg) is trapped by a square barrier that has width 2.0 fm and height 30 MeV.
What is the tunneling probability if the kinetic energy of the alpha particle is 1.0 MeV below
the top of the barrier ?
Here G= 0.5 and the tunneling probability
T= 0.09 or 9%Remember to convert to MKS units for
kappa
7
1
eV
=1.6 x 10
-19
J
Slide8Example of QM Tunneling and alpha decay (III)
An alpha particle (m=6.64 x 10-27kg) is trapped by a square barrier that has width 2.0 fm and height 30 MeV.
What is the tunneling probability if the kinetic energy of the alpha particle is 1.0 MeV below
the top of the barrier ?The tunneling probability T= 0.09 or 9% for an alpha 1.0 MeV below the top of the well T=0.014 or 1.4% for a particle 10 MeV below the barrier (energy 20 MeV)
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Slide9The key to understanding energetics of nuclear reactions.
Question: This equation is based on E=mc
2
. Do you see why ?Question: What is Q if Q is positive ?Ans: Energy release Question: What is Q if Q is negative ?Ans: Energy that must supplied to make the reaction proceed.
Slide10Example:
The difference between the LHS and RHS is -0.00128u
If Q is negative, what is the energy release ?
Ans: Must supply 1.192 MeV to A+B in center of mass for the reaction to proceed.
What is u (and why are the values not exact integers ?
Slide11The atomic mass unit is defined so that C12 has exactly 12 u
Question: Why is MAZ not exactly equal to the sum of (Z x M
p) + (N x Mn
) ? Ans: There is nuclear binding energy !
Slide12Some consequences of this curve of binding energy
Slide13165 MeV
7 MeV
6 MeV
7 MeV6 MeV9 MeV200 MeV~ kinetic energy of fission products~ gamma rays~ kinetic energy of the neutrons
~ energy from fission products~ gamma rays from fission products
~ anti-neutrinos
from fission products
energetics
Each U-235 fission releases 30 million times more energy than a molecule of TNT;
3 million times per mass than coal
Energetics
But need one neutron to interact with the U-235 each time
Slide14Nuclear Power is based on a chain reaction involving fission
Based on fission induced by neutrons
Nucleus is like a droplet of nuclear matter with surface tension from strong interaction and EM Coulomb repulsion from protons in competition
N.B. This does not work for U-238
Difference in rest mass here
Slide15Nuclear stability and radioactivity
The right figure is a
Segr
è chart showing N versus Z for stable nuclides.In α decay, Z decreases by 2 and A decreases by 4, (why ?) moving the nuclei closer to the line of stability.
15
Slide16Why do stable nuclei with many nucleons (those with a large value of
A
) have more neutrons than protons?
Nuclear Stability Clicker Question A. An individual nucleon interacts via the nuclear force with only a few of its neighboring nucleons.B. The electric force between protons acts over long distances.C. The nuclear force favors pairing of both neutrons and protons.D. both A. and B.E. all of A., B., and C.
16
Slide17Why do stable nuclei with many nucleons (those with a large value of
A
) have more neutrons than protons?
Nuclear Stability Clicker Question A. An individual nucleon interacts via the nuclear force with only a few of its neighboring nucleons.B. The electric force between protons acts over long distances.C. The nuclear force favors pairing of both neutrons and protons.D. both A. and B.E. all of A., B., and C.
17
The Coulomb (EM ) interaction is infinite range while the strong force is short-range
Slide18Nuclear spin
Like electrons, protons and neutrons are spin ½ particles. Spin and total angular momentum are quantized
Question: What is S for a single nucleon ?
Question: What is SZ for a single nucleon ?
18
Slide19Nuclear spin
The total angular momentum is the sum of the spin and orbital angular momentum of all nucleons.
19
Slide20Nuclear magnetic moments and a mystery
There is also a nuclear magneton.
Question: How does this compare to the Bohr
magneton ?Ans: It is 1836 times smaller than μB because of the ratio of the electron and proton mass (x 1836 heavier).Question: Shouldn’t the proton z component be +- μn ? And shouldn’t the neutron be zero ? What is going on ?
Ans: quarks
20
Slide21Importance of nuclear spin
21
Slide22Important applications of nuclear spin
What is this called ?
Ans
: Nuclear Magnetic Resonance (NMR)
22
Slide23Importance of nuclear spin
23
Slide24Radioactive decay: Activities and half-lives
The
half-life is the time for the number of radioactive nuclei to decrease to one-half of their original number
. The number of remaining nuclei decreases exponentially with decay constant λ (see Figure on the right).Activity is measured in either Curies (US) or Becquerel (Europe or Japan) 1 Ci= 3.7 x 1010Bq =3.7 x 1010decays/sec
24
Slide25Radioactive decay law
Here N(t) is the number of radioactive nuclei present. The quantity
λ
is the “decay constant” and determines the probability per unit time that a nuclei will decay.Question: How do we integrate this ?Question: What is the solution ?
25
Slide26Radioactive decay law
What is the half-life ? This corresponds to N(t)/N0=1/2
26
N.B. Half-life is different from the lifetime !!
Slide27Q38.1
Yes, it can occur because it balances both charge number and mass number.
Yes, it
it can occur because the total rest mass of the product is greater than the rest mass of the original particle.No, it it cannot occur because the total rest mass of the product is greater than the rest mass of the original particle.No, it it cannot occur because the total rest mass of the product is smaller than the rest mass of the original particle.
27
Hint:
m_p
=1.007276 u,
m_n
= 1.008665 u
Slide28Q38.1
Yes, it can occur because it balances both charge number and mass number.
Yes, it
it can occur because the total rest mass of the product is greater than the rest mass of the original particle.No, it it cannot occur because the total rest mass of the product is greater than the rest mass of the original particle.No, it it cannot occur because the total rest mass of the product is smaller than the rest mass of the original particle.
28
Hint:
m_p
=1.007276 u,
m_n
= 1.008665 u