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Stable vs. Unstable

- In some atoms, the binding energy is great enough to hold the nucleus together. The nucleus of this kind of atom is said to be stable.
- In some atoms the binding energy is not strong enough to hold the nucleus together, and the nuclei of these atoms are said to be unstable.
- Unstable atoms will lose neutrons and protons as they attempt to become stable.
- Unstable atom radioactive atom

Stable nucleus – non-radioactive

- Unstable nucleus – radioactive
- less stable means more radioactive
- more stable means less radioactive.

Q: What makes the nucleus a stable one?

- It appears that neutron to proton (n/p) ratio is the dominant factor in nuclear stability.
- This ratio is close to 1 for atoms of elements with low atomic number and increases as the atomic number increases.

Q: How do we predict the nuclear stability?

- Predicting the nuclear stability is based on whether nucleus contains odd/even number of protons and neutrons

less stable means more radioactive

more stable means less radioactive

Q: Based on the even-odd rule, predict which one would you expect to be radioactive in each pair?

- 16/8 O and 17/8 O

(b) 35/17 Cl and 36/17 Cl

(c) 20/10 Ne and 17/10 Ne

(d) 40/20 Ca and 45/20 Ca

(e) 195/80 Hg and 196/80 Hg

A.

(a) The 16/8O contains 8 protons and 8 neutrons (even-even) and the 17/8O contains 8 protons and 9 neutrons (even-odd). Therefore, 17/8O is radioactive.

(b) The 35/17Cl has 17 protons and 18 neutrons (odd-even) and the 36/17Cl has 17 protons and 19 neutrons (odd-odd). Hence, 36/17Cl is radioactive.

(c) The 20/10Ne contains 10 protons and 10 neutrons (even-even) and the 17/10Ne contains 10 protons and 7 neutrons (even-odd). Therefore, 17/10Ne is radioactive.

(d) The 40/20Ca has even-even situation and 45/20Ca has even-odd situation. Thus, 45/20Ca is radioactive.

(d) The 195/80Hg has even number of protons and odd number of neutrons and the 196/80Hg has even number of protons and even number of neutrons. Therefore, 195/80Hg is radioactive.

Again: Nuclear Binding Energy

- The nuclear binding energy is an energy required to break up a nucleus into its components protons and neutrons.
- … converts some of the masses of protons and neutrons into an energy and
- … utilizes that energy to bind the protons and neutrons within the nucleus.
- If we know how much mass (aka, mass defect) is utilized– to bind/build the nucleus
- we can convert it into binding energy using the Einstein’s equation:
- E=mc2 m=mass, c=velocity of light

http://faculty.ncc.edu/LinkClick.aspx?fileticket=sSPFB6xEtbM%3D&tabid=1918

Exa. – Nuc Binding Energy

- Consider that 56/26 Fe has an atomic mass of 55.934942 amu (experimental) [26 p / 30 n]

Mass of proton (1/1H ) : 1.007825 amu

- Mass of neutron (1/0n) : 1.008665 amu

Mass of 26 p = 26 x 1.007825 = 26.20345 amu

Mass of 30 n = 30 x 1.008665 = 30.25995 amu

Total 56.46340 amu

This mass is larger than 55.934942 amu (experimentally determined mass) by 0.52846 amu.

Mass defect: The difference between experimental mass of the atom and the sum of the masses of its protons, neutrons, and electrons is known as mass defect [md]

md = mass of products – mass of reactants

= experimental mass of an atom – calculated mass of an atom

= 55.934942 amu – 56.46340

= - 0.52846 amu

As a consequence, the calculated energy will also be negative because the formation of 56Fe from 26 protons and 30 neutrons is an exothermic reaction meaning that the energy is released to the surrounding.

- This mass defect can be further transformed into energy using Einstein’s equation:

Change in energy [Jule] = mass defect [amu]*c2

E = [mass defect] X 1.4945 x 10-10 J/amu

= -0.528458 amu x 1.4945 x 10-10 J/amu

= - 7.8978 x 10-11 J/ nucleus

This is the amount of energy released when one iron-56 nucleus is created from 26 protons and 30 neutrons.

So, the nuclear binding energy for this nucleus is 7.8978 x 10-11 J,

which is also the amount of energy required to decompose this nucleus into 26 protons and 30 neutrons.

Therefore, the nuclear binding energy for 1 mole of iron-56 is 4.7560 x 1010 kJ (this is about 48 billion of ), which is a tremendous amount of energy!

http://faculty.ncc.edu/LinkClick.aspx?fileticket=sSPFB6xEtbM%3D&tabid=1918

Some Units

- ActivitybecquerelBq s-1
- Absorbeddose gray Gy J/kg m2·s-2
- DoseequivalentsievertSv J/kg m2·s-2
- barn b 1b = 100 fm2= 10-28m2= 10-24cm2
- curie Ci 1 Ci = 3.7×1010Bq
- roentgen R 1R = 2.58×10-4C/kg
- rad rad 1 rad = 1 cGy = 10-2Gy
- rem rem 1 rem= 1 cSv= 10-2Sv
- 1 kWh = (1000 W)×(3600 s) = 3.6×106J
- 1 mmHg = 1 Torr = (1/760) atm = 133.322 Pa

Some Units in Reactor Physics

- Very often, centimeter will be used rather than meter.
- Mass density in g/cm3: ρw≈1 g/cm3
- Number density:#/cm3: n= 1012n/cm3; N= 1024atom/cm3
- Velocity in m/s: vth= 2200 m/s
- Energy in eV: εf≈ 200 MeV per 1 fission of 235U

Nuclear reactions

a + X Y + b

Here,

a is an incident particle,

X is a target nucleus,

Y is a residual nucleus,

b is an emitted particle.

Reactions where no ais involved are called decays [alpha, beta, gamma decays or rays].

- Before and after the nuclear reaction, the total energy and momentum are conserved for the system.

Radioactivity

- The capability to emit radiation is called radioactivity.
- Radioactive strength is expressed by the unit becquerel (Bq), an SI unit.
- One decay per second 1 Bq.
- The traditionally used unit, the curie (Ci), is still frequently used.

1 Ci = 3.7 × 1010Bq

C – curie

- The basic unit of measure for describing the activity (radioactivity) of a quantity of radioactive material is the curie
- A quantity of radioactive material is considered to have an activity of 1 curie or 1 C, when 37 billion of its atoms decay (disintegrate) in 1 sec.
- 1C = 3.7 X 1010 disintegrations/sec.

Radioactivity

- Atoms with unstable nuclei are constantly changing as a result of the imbalance of energy within the nucleus.
- When the nucleus loses a neutron, it gives off energy and is said to be radioactive.
- Radioactivity is the release of energy and matter that results from changes in the nucleus of an atom.

Radioactive isotopes are often called radioisotopes.

- All elements with atomic numbers > 83 are radioisotopes

meaning that these elements have unstable nuclei and are radioactive.

- Elements with atomic numbers of 83 and less, have isotopes (stable nucleus) and most have at least one radioisotope (unstable nucleus).
- As a radioisotope tries to stabilize, it may transform into a new element in a process called transmutation.

Radioactive decay

- Radioactive decay is the spontaneous breakdown of an atomic nucleus resulting in the release of energy and matter from the nucleus.
- Radioisotopes would like to be stable isotopes so they are constantly changing to try and stabilize.
- In the process, they will release energy and matter from their nucleus and often transform into a new element.
- This process, calledtransmutation, is the change of one element into another as a result of changes within the nucleus.

The radioactive decay and transmutation process will continue until a new element is formed that has a stable nucleus and is not radioactive.

- Transmutation can occur naturally or by artificial means.

Alpha/Beta/Gamma decay

- 3 decays but their order of likelihood is

γ-decay,

β-decay,

α-decay.

- In γ-decay, the nucleus does not change.

Alpha/Beta/Gamma decay

- Alpha decay:

U238 Nucleus Thorium-234 + alpha decay

Alpha particle 2p + 2n

- Beta decay: C-12 [6p, 6n]; C-14 [6p, 8n]

Carbon-14 nucleus –

In beta decay, a neutron from an atom will split into one positively charged proton & a negatively charged electron

C-14 [6p, 8n, 6e] ??[6+1p, 8-1n, 1e] N-14 [7p, 7n, 7e]

So, Carbon-14 Nitrogen-14 nucleus

1n 1p + 1e

Gamma decay

Uranium-238 nucleus

- Alpha & beta decay are almost always accompanied by Gamma decay.
- Here, energy in the form of gamma radiation or rays is radiated from nuc.
- … are electromagnetic waves with very high frequencies & energy.
- … are identical to X-rays, artificially produced; gamma rays are naturally occurring.
- Both X-ray or gamma rays are dangerous to life!

Nuclear vs. Chemical reactions

- The principle difference between them lies in how the reaction occurs, specifically how the atom is affected.
- Chemical reactions involve an atom’s electrons
- Nuclear reactions involve the atom’s nucleus.

Radioactive half-life

- Not all of the atoms of a radioisotope decay at the same time, but they decay at a rate that is characteristic to the isotope.
- The rate of decay is a fixed rate called a half-life.
- … how long it takesfor half of the atoms in a given mass to decay.

Some isotopes decay very rapidly and, therefore, have a high specific activity.

- Others decay at a much slower rate.

Polonium-215 0.0018 seconds

Bismuth-212 60.5 seconds

Sodium-24 15 hours

Iodine-131 8.07 days

Cobalt-60 5.26 years

Radium-226 1600 years

Uranium-238 4.5 billion years

How does the half-life affect an isotope?

- Lets, 10 grams of Barium-139.
- It has a half-life of 86 minutes.
- After 86 min, half of the atoms in the sample would have decayed into another element, Lanthanum-139.
- So, after one half-life, 5 gr of Barium-139, & 5 gr of Lanthanum-139.

- Half of the 5 grams of Barium-139 would decay into Lanthanum-139.
- So, 2.5 grams of Barium-139 & 7.5 grams of Lanthanum-139!
- Carbon-dating -- read

- After 4.5 billion yrs [U-238’s life-time]

?

Half of the U-238 atoms have decayed to Thorium atoms!

How deep will radiation penetrate into a material?

- Radiation has a more difficult time penetrating dense materials, such as metal than it does less dense materials, such as plastic.

Neutron Nuc reactions

- Compared with chemical reactions, nuclear reactions are much less likely to occur.

Why?

- A nucleus is much smaller than an atom and molecule, and collisions are less likely to take place.
- Nuclei are positively charged, and thus have difficulty in approaching each other because of the repulsive Coulomb force.
- High energy is usually required to overcome the Coulomb force.

Rd.

Moreover,

- when the energy is low,
- quantum mechanics dictates that the wavelength increases, &
- thus reactions can often take place more easily.
- According to de Broglie, a neutron with momentum phas the following wavelength:

λ = h／p

where,h is Planck’s constant

Rd.

- If we use energy instead of momentum, we obtain the following:

λ = 2.86×10−11E−1/ 2(m)

This energy is extremely large compared with that of a nucleus.

Isolated neutron

- Although a neutron inside a stable nucleus is stable, an isolated neutron changes to a proton by β-decay.
- The half life of an isolated neutron is short, only 10.37 minutes…
- However, this is long when we consider the behavior of neutrons inside a nuclear reactor.

fission

- The main forces operating inside a nucleus are due to the volume term and surface term.
- This causes the nucleus to behave like a liquiddrop.
- Therefore, if energy is applied from the outside, oscillation modes are excited in the same way as for a liquid drop.
- In this way, a nucleus can fission into two pieces, which is the process known as nuclear fission.

This type of nuclear fission is observed in heavy nuclei.

- Among the naturally-occurring nuclides, 235U can fission by thermal neutrons - best.
- If the energy of the neutrons is increased, 238U and 232Th can fission.

Nuclear fission by a thermal neutron is called thermalfission and

- Nuc fission by a fast neutron is called fast fission.
- Thermally fissionable material is called fissile material (233U, 235U, 239Pu, and 241Pu)

The only naturally-occurring elements that are useful as nuclear fuel are uranium - U and thorium - Th.

- Uranium of natural composition is called naturaluranium.
- Natural uranium contains 0.0054% 234U, 0.720% 235U, and 99.275% 238U.
- Natural thorium contains 100% 232Th.

Neutron flux

- When we consider a reaction of a neutron and a nucleus, the probability that the reaction takes place is considered to be proportional to

- the size of the nucleus and

- the distance that the neutron travels per unit time.

Thus, to express the quantity of neutrons, it is more convenient to use the product of the neutron number density nandthe velocity v

φ (r, E, t) = vn (r, E, t)

- This quantity is called the neutron flux.

Radiation detection

Types –

- Methods based on the detection of free charge carriers

ionization chamber, proportional counters, Geiger-Muller counters, etc.

scintillation counter, Cerenkov counter

3. Based on the visualization of the tracks of the radiation

cloud chamber, bubble chamber, spark chamber

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