19.1 Nuclear Chemistryfaculty.sdmiramar.edu/fgarces/zCourse/All_Year/Ch...Calculation of Age Based on t 1/2 TURIN, Italy -- Almost everything about the Shroud of Turin is mysterious-

February 14 1 RadioActivity

19.1 Nuclear Chemistry

Radio Activity

Dr. Fred Omega Garces Chemistry 100 Miramar College


One Winter Day in Chicago

The first self-sustaining nuclear fission reactor was build on a squash court at the University of Chicago. This accomplishment led to the development of the first atomic bomb at Los Alamos National Laboratory in New Mexico in July 1945. This was the dawn of the Nuclear Age. Enrico Fermi was the director.

The Chain Reaction. Construction halted with the fifty-seventh layer on December 1, when measurements indicated the pile would become self-sustaining should the control rods be withdrawn. On December 2, Fermi and his colleagues gathered on the balcony of the squash court to test the reactor, slowly withdrawing the last control rod until the "critical," or self-sustaining, level was reached, then watching the reactor operate for twenty-eight minutes before reinserting the rod and stopping the reaction. Compton telephoned the news to Harvard president James B. Conant, member of the Manhattan Project Military Policy Committee, with the coded message, "The Italian navigator has just landed in the New World."


Discovery of Radioactivity 1897 Antonio Henri Becquerel

Provided the relationship between phosphorescence and X-Rays. Becquerel discovered radiation by accidentally placing a Uranium rock on a photographic plate. He discovered that the rock emitted radiation because of photographic plate exposure.

1898 Maria Curie Is credited for naming the strange radiation radioactivity. She went on and won two Noble Prizes for the discovery of Radium and Polonium. Later her daughter also won a Noble Prize.


Radioactivity Nucleons - the subatomic particles in the nucleus: Protons & Neutrons Isotopes - atoms with different number of neutrons in the nucleus but the same

number of protons or atomic number (Z). Isotopes of carbon : 11C, 12C, 14C or C-11, C-12, C-13, C-14 (note that Z=6) Uranium Isotopes: U-233, U-235, U-238 (note that Z= 92)

The numerical suffixes represent the mass number, A ( Mass number you recall is represented by A; A = protons + neutrons)

Radionuclides- Nuclei that are radioactive. Radioisotopes - Atoms containing radionuclides

In a Nuclear Equation, the total number of nucleons is conserved

238U g 234 Th + 4 He 92 90 2 238 Mass number = 234 + 4

92 Atomic number = 90 + 2

131I g 131 Xe + 0 e 53 54 -1 131 Mass number = 131 + 0

53 Atomic number = 54 + (-1)


Subatomic Particles Nomenclature Particle Charge Mass (g) Nomenclature alpha 2+ 6.64e-24 4 He 4 α

2 2

beta 1- 9.11e-28 0 e 0 β -1 -1

gamma 0 0 0 γ proton 1+ 1.673 e-24 1 H 1 p

1 1 neutron 0 1.675 e-24 1 n

0 electron 1- 9.11e-28 0 e

-1 positron 1+ 9.11e-28 0 e

+1


Radionuclides - spontaneously emit particles and radiation which can be expressed by a nuclear equation

Spontaneous Emission: Mass and charge are conserved.

Alpha emission Beta emission

Gamma emission Positron Emission

Electron capture

Nuclear Equation: Emission

€

92238U → 90

234Th + 24 He

€

53131I → 54

131Xe + -10e

€

01n → 1

1p + -10e

€

92238U → 90

234Th + 24 He + 0

0γ

€

611C → 5

11B + 10e

€

11p → 0

1n + 10e

€

11p + -1

0e → 01n

€

24 He

€

+10e

€

00γ

€

-10e (product)

€

-10e (reactant)


Radiation Property α β γ

Charge +2 -1 0 Mass(g) 6.64e-24 9.11e-28 0

Penetrating Power 1 100 10,000 Description Low Moderate High Piece paper piece wood Lead wall

Velocity 5-7% C > 90% C C Nature of radiation 4 He 0 e 0 γ 2 -1 0


Patterns of Nuclear Stability

Belt of Stability- Neutrons are believed to hold the protons together in the nucleus, like glue. As the atomic mass increases, the neutron to proton ratio increases because proton-proton repulsion becomes more significant. Therefore the neutron to proton ratio must increase for heavier elements. (Note that the belt of stability has a slope greater than 1 indicating an increasing neutron to proton ratio for larger atoms.


Belt of Stability: A closer look

A plot of neutrons vs. protons for the stable nuclides. A plot of N vs. Z for all stable nuclides gives rise to a narrow band that veers above N/Z=1 shortly beyond Z=10. The N/Z values for several stable nuclides are given. The most common modes of decay for unstable nuclides in a particular region are shown: nuclides with a high N/Z ratio often undergo β decay; those with a low ratio undergo e- capture or Positron emission; heavy nuclei beyond the stable band (and a few lighter ones) undergo α decay.

The blue box in the larger diagram is expanded to show the stable and many of the unstable nuclides in that area. Note the modes of decay; α decay decreases both N and Z by two; b decay decreases N and increases Z by one; Positron emission and e- capture increase N and decrease Z by one.

Neu

tron

s (N

)


Pattern to Stability Radioactive decay leads to particles which lie in the Belt of stability

Above Belt - β-emitters (High n:p) neutron-rich lowers ratio and move right towards belt of stability.

Below Belt - electron capture or positron emitters (Low n:p) proton-rich raise ratio and move left toward belt of stability.

Nuclei with Z > 83 tend to be α -emitters Heavy nuclei decrease both proton and neutron.


Other Considerations

Other Factors to Nuclear Stability • Magic number

Protons with - 2, 8, 20, 28, 50 or 82 Neutrons with - 2, 8, 20, 28, 50, 82 or 126

• Nuclei with even # of protons and neutrons are more stable than with any odd number of protons and neutrons.

• Shell model of the nucleus explains these observation.

• Magic number correspond to filled, closed-shell nucleon configuration.

• Pairs of protons and neutrons analogous to pair of electrons in the atom.


Radioactive Series Predicting Nuclear Stability -

Radionuclides sometimes go through a series of emission (Radioactive series) before becoming a stable nuclei.

Nuclear disintegration series for U-238 under goes α-emission (blue arrows) and β-emission (red arrows) until it forms stable Pb-206 (which is an isotope within the belt of stability.


Transmutation - Change of nuclear identity by artificially striking nucleus with a particle. • Many medical chemotherapy isotopes are formed by transmutation. • Many new elements are discovered by transmutation

Nomenclature: Target (bombard, ejected) product 8

17O + 11H g 24He + 714N In this example, The target is 17O, the product is 14N, the bombarding particle is a proton 1H (or p) and the ejected particle is the alpha particle 4He (or α). The nomenclature is therefore

17O (p,α) 14N

Example: solve the following. The answer is in the next slide.

i) 238U + 1n g 239Np + 0β ( see next slide for answer) ii) 238U (n,γ) 239U ( see next slide for answer) iii) 18O (n,β) 19F ( see next slide for answer)

Nuclear Transmutation


Particle Accelerators - Slamming particles into nuclei leads to synthesis of different or new elements • Cyclotrons or synchrotron

Transmutation: Charge and neutral particles

Chemotherapy Application

Answer for previous problems: (i) 238U(n, β) 239Np (ii) 238U + 1n g γ + 239U (iiii) 18O + 1n g 0β + 19F


Transmutation: Transuranium

Artificial transmutation used to produce elements above 92. Neutron projectiles are bombardment source. These come from radioactive isotopes. 238U + 1n g 239U g 239Np + -10e 239Np g 239Pu + -10e

Example 21.55 a) 235U + 1n g 160Sm + 72Zn + ? 1n b) 239Pu + 1n g 144Ce + ? + 2 1n

Example 21.56 b) 233U + 1n g 133Sb + 98Nb + ? 1n


Rates of Radioactive Decay • Radioactive substance possess special rates of decay and half

lives, t1/2 . • Radioactive decay is a first-order kinetic process. ln {N/No} = -k t t1/2 = 0.693/ k

Half-life - The time in which

a substance will decay to one-

half its original mass.


Radioisotope Half-Lives Each isotope has its characteristic half-life unaffected by external conditions, i.e., temp, pressure, chemical nature.

Half-Lives and Type of Decay for Several Radioisotopes. Isotope Half-life (yr) Type of Decay

Natural radioisotopes 238U 4.5 •109 Alpha

235U 7.1•108 Alpha

232Th 1.4•1010 Alpha

1940K 1.3•109 Beta

614C 5,730 Beta

Synthetic radioisotopes 94239Pu 24,000 Alpha

55137Cs 30 Beta

3890 Sr 28.8 Beta

53131I 0.022 Beta


Radioisotope Dating For 1st Order Reaction: Half-life is independent of concentration of reactant. C-14 dating is accurate only up to 50,000yr. 14C g 14N + -1e β-emission U-238 accurate up to 4.5•109 yr. Based on data, Earth is 4-4.5 Billion yrs old.

€

t12

= ln2k

ln[A] = - kt + ln[A]o

€

ln [A]o

[A]o2

"

# $

%

& '

= k ⋅t1 /2

Otzi the iceman, discovered Sept ‘91, Carbon dating ~ 5300 yrs old http://www.crystalinks.com/oetzi.html

Otzi The Iceman


Calculation of Age Based on t1/2 TURIN, Italy -- Almost everything about the Shroud of Turin is mysterious- its age, its authenticity, and the identity of the bearded man with deep-set eyes whose image is imprinted on the 14-foot length of yellowing linen, still believed by many Christians to be the burial cloth of Jesus. ....as carbon testing done on tiny swatches of the shroud concluded in 1988 -- or to the time of Jesus, the centuries-old fascination with the shroud....

€

t12

= ln2k

t12

= 5730 yr

k = ln2t

12

=ln2

5730 yr=

0.6935730 yr

= 1.21•10-4 yr−1

€

12 C14 C

=1012

1

14 C[ ]= 50.000 ppt based on 12C

14 C[ ]= 46.114 ppt today

€

Ao = 50.000A = 46.114

" # $

= lnAoA

= kt

€

ln50.00046.114

1.21• 10−4 yr−1 = t

€

t = 668.6 yr

€

1990 -669 = 1321 ±50 AD

The Shroud of Turin is a linen cloth over 4 m long. It bears a faint, straw-colored image of an adult male of average build who had apparently been crucified. Reliable records of the shroud date to about 1350, but for these past 600 years it has been alleged to be the burial shroud of Jesus Christ. Numerous chemical and other tests have been done on tiny fragments of the shroud in recent years. The general conclusion has been that the image was not painted on the cloth by any traditional method, but no one could say exactly how the image had been created. Re-cent advances in radiochemical dating methods, however, led to a new effort in 1987–1988 to estimate the age of the cloth. Using radioactive 14 C, the flax from which the linen was made was shown to have been grown between 1260 and 1390 A.D. There is no chance that the cloth was made at the time of Christ.


Rates of Radioactive Decay Example: The half life for 238U g 206Pb is 4.5•109 yr. A mineral

sample contains 50.0 mg of 238U and 14.0 mg of 206Pb. What is the age of the mineral? Original U = 50 mg U + 14.0 mg Pb • 238 U = 66.2 mg U 206 Pb

For First order Kinetics: ln[A] = - kt + ln[Ao]

t1/2 = ln2 k = 0.693 = 1.5•10-10 yr -1 k 4.5•109 yr

ln[A] = - kt + ln[Ao] kt = ln [Ao] - ln[A]

kt = ln [Ao] [A]

t = 1 ln [Ao] k [A]

t = 1 ln [Ao] = 1 ln 66.2 k [At ] 1.5•10-10 yr-1 50.0

t = 1,871,049,717 yrs t = 1.9 •109 years or 1.9 billion years


Rates of Radioactive Decay Example: The half-life of U-238 is 4.5•109 yr. A sample of rock of mass 1.7 g is found to produce 31 dis/s. Calculate the % mass 238U.

Rate = k [N], %238 U = N

No

⋅100, No = 1.7 g

k = 0.693t

1/2

= 0.6934.5 ⋅109 yr

= 1.54 ⋅10-10 yr-1

31 diss

• 60 s1 min

• 60 min1 hr

• 24 hr1 day

• 365.25 day1 yr

• 1 atom1 dis

• 1 mole6.02 ⋅1023 atom

•238 g U1 mole

= 3.868 ⋅10-13 gyr

Rate = K[N] → [N] = RateK

= 3.868 ⋅10-13 g

yr1.54 ⋅10−10 yr−1

= 3.285 ⋅10-4 g

% mass 238 U = 3.285 ⋅10-4 g1.7g

•100 = 0.148 %


Summary Radioactivity Process

Type of Radiation

α, β, γ, positron

Nuclear Equation

Nucleons are conserved

Nuclear Stability

Greater Z, the higher n:p ratio

Transmutation

Changing atomic identity

Rates of Decay

Radioactivity follows first order Kinetics

Documents

19.1 Nuclear Chemistryfaculty.sdmiramar.edu/fgarces/zCourse/All_Year/Ch...Calculation of Age Based on t 1/2 TURIN, Italy -- Almost everything about the Shroud of Turin is mysterious-