Nuclear Reactions
Nuclear reactions involve changes that take place within atomic nuclei (the transmutation of elements).
Ordinary chemical reactions involve changes in the outer electronic structures of atoms or molecules.
Nuclear reactions are represented by nuclear equations.
Nuclear equations must be balanced with respect to nuclear charge (atomic number) and nuclear mass (mass number).
Example: 147 N + 10 n ---à 146 C + 11 H
The atomic numbers add to 7 on both sides and the mass numbers add to 15 on both sides.
Radioactivity
A radioactive nucleus decomposes (decays) with the evolution of energy.
Many nuclei exhibit natural radioactivity, others can be made in the lab by bombarding stable nuclei with high-energy particles.
Modes of Decay:
(1) alpha (α) particle emission – an ordinary helium nucleus (42 He) is given off
Ex: 23892 U ---à 42He + 23490 Th
(2) beta (β) particle emission – an electron is produced (0-1 e )
Ex: 23490 Th ---à 0-1 e + 23491 Pa
The atomic number increased by one unit. Beta emission converts a neutron to a proton (in nuclei that have too many neutrons for stability).
(3) gamma (γ) radiation emission – high energy photons – omitted from nuclear equations (as it does not change atomic # or mass)
Artificially produced radio active nuclei can exhibit α, β, or γ-emission, additionally they can exhibit:
(1) positron emission – a particle identical to an electron with a +1 charge (01 e).
Ex: 4019 K --à 01 e + 4018 Ar
The atomic number decreases by one unit. A proton is converted to a neutron, when nuclei have too many protons for stability.
(2) K-electron capture - an electron in the inner most energy level (n=1) falls into the nucleus – common with heavy nuclei because n=1 is closer to the nucleus
Ex: 8237 Rb + 0-1 e ---à 8236 Kr
The result of K-electron capture is the same as positron emission (atomic # decreases by one unit).
Example
Promethium (Z = 61) is essentially nonexistent in nature; all of its isotopes are radioactive. Write balanced nuclear equations for the decomposition of (a) Pm -142 by positron emission. (b) Pm-147 by beta emission. (c) Pm-150 by alpha emission.
Bombardment Reactions
More than 1500 isotopes have been prepared in the laboratory by bombardment reactions.
In these reactions a stable nucleus is convert to one that is radioactive, which in turn decays to stable products.
The bombarding particle can be:
(1) neutron (at low energy produced by a fission reactor)
Ex: 2713 Al + 10 n --à 2813 Al
2813Al --à 2814Si + 0-1 e (beta emission)
(2) a charged particle (electron, positron, α-particle, etc.) accelerated to high velocity in an electric and/or magnetic fields
Ex: 2713 Al + 42 He ---à 3015P + 10n
3015P --à 3014Si + 01e (positron emission)
An application of bombardment reactions is the preparation of transuranium (greater atomic # than uranium) elements (107 -112 and 114 in 1999 t1/2 = 30s).
Applications
I. Medicine
A. Cancer therapy – radioactive isotopes (like Co-60) produce γ-rays that are focused on malignant cells
Thyroid cancer can be treated by having a patient drink a solution of NaI (with radioactive iodide- 131Ior 123I). The iodine moves to the thyroid and the radiation destroys malignant cells.
B. Radioactive nuclei used for diagnosis – Positron emission tomography (PET) using C6H12O6 containing C-11, a positron emitter, to study the brain. Radioisotopes are used for test for anemia (5926 Fe), circulatory disorders (2411 Na), and lung disorders (13354 Xe) among many others.
II. Chemistry
A. Chemical analysis like neutron activation analysis (a sample is bombarded with neutrons forming a radioactive isotope that decays by gamma emission - the wavelength of the gamma ray varies by element and can be used for quantitative analysis)
8438Sr + 10 n ---à 8538 Sr
III. Commercial
A. Smoke alarms- Smoke impedes the flow of air molecules ionized by Am-241 in an ionization chamber, causing current to drop and the alarm to sound.
B. Food irradiation – Gamma rays are used to kill insects, larvae, and parasites (trichina). Radiation can also inhibit sprouting and kill microorganisms (E. coli). Shelf-life can be extended by weeks or even months.
Rate of Radioactive Decay
Radioactive decay is a first order process.
rate = kX
ln X0 = kt
X
k = 0.693
t1/2
k = first order rate constant, X0 = amount of radioactive species at t=0, X = amount at time t, t1/2 = half-life
Rate of decay is often expressed by the activity (A) of the sample, which expresses the number of atoms decaying in unit time.
A = kN
A = activity, k = rate constant, N = # of radioactive nuclei present
Activity can be expressed in:
1 becquerel (Bq) = 1 atom/s
1 curie (Ci) = 3.700 x 1010 atoms/s
Example
The half-life of radium-226 is 1.60 x 103 y = 5.05 x 1010 s. (a) Calculate k in s-1 (b) What is the activity in curies of 1.00 g of Ra-226? (c) What is the mass in grams of a sample of Ra-226 that has an activity of 1.00 x 109 atoms/min?
Carbon Dating
The age of organic material can be determined based on the decay rate of C-14.
147 N + 10n --à 146C + 11H
146C --à 147 N + 01e (t1/2 = 5730 y)
1 for every 1 x 1012 atoms of C in CO2 is C-14.
ln A0 = kt
A
A0 = original activity (13.6 atoms/min), A = measured activity today, t = age of sample
Example
A tiny piece of paper taken from the Dead Sea Scrolls, believed to date back to the first century A.D., was found to have an activity per gram of carbon of 10.8 atoms/min. Taking A0 to be 13.6 atoms/min, estimate the age of the scrolls.
Mass –Energy Relations
The energy change accompanying a nuclear reaction can be calculated from the relation:
ΔE = c2Δm
m = mass products-mass reactants
ΔE = energy products- energy reactants
c = speed of light
A spontaneous nuclear rxn is exothermic, ΔH and ΔE are negative, and Δm is negative.
Δm is very small in an ordinary chemical rxn but in a nuclear rxn it can be around 0.002 % of the mass of the reactants.
ΔE = c2Δm
c = 3 x 108m/s
ΔE = 9.00 x 1016 m2/s2 x Δm
1 J =1 kg ∙ m2/s2 ; 1 m2/s2 = 1 J/kg
ΔE = 9.00 x 1016 J/kgx Δm or
9.00 x 1010 kJ/g x Δm
Example
For the radioactive decay of radium, 22688Ra -à 22286Rn + 42He, calculate ΔE in kilojoules when 10.2 g of radium decays.
Nuclear Binding Energy
A nucleus weighs less than the individual protons and neutrons of which it is composed.
Example:
63Li = 3 p+ and 3 n0 = 3 (1.00867 g) + 3 (1.00728 g) = 6.04785 g – total mass of 3 moles of p+ and n0
A nuclear mass table lists one mole of Li-6 nuclei as 6.01348 g.
One mole of Li-6 weighs less than the corresponding protons and neutrons.
63Li ---à 3 11H + 310n
Δm = 6.04785g -6.01348g = 0.03437 g/mol Li
This is the mass defect. The energy difference is 3.09 x 109kJ/mol Li.
This energy is referred to as the binding energy.
3.09 x 109kJ are absorbed to decompose one mole of Li-6 nuclei into protons and neutrons. The same amount or energy is evolved when one mole of Li-6 nuclei form from protons and neutrons.
The binding energy reflects the stability of the nucleus.
A good measure of relative stabilities of different nuclei is the binding energy per mole of nuclear particles (nucleons), calculated by dividing the binding energy per mole of nuclei by the number of particles in the nucleus.
Example:
Li-6
3.09 x 109 kJ x 1mol Li-6 = 5.15 x 108 kJ/mol
mol Li-6 6 mol nucleons
Example
Calculate the binding energy of C-14, in kilojoules per mole using published nuclear mass values.
Nuclear Fission
Nuclear fission is the process by which a heavy nucleus is split into smaller nuclei, releasing energy in the process.
Fission takes place when elements are bombarded with neutrons of high enough energy.
23592U and 23994Pu are the most common isotopes used for the process.
Example:
More than 200 isotopes of 35 elements have been identified among the fission products of U-235.
9037Rb + 14455Cs + 2 10n
10n + 23592U ----à 8735Br + 14657La + 3 10n
7230Zn + 16062Sm + 4 10n
The products are often radioisotopes can pose radiation hazards.
Two to four neutrons are produced for every one consumed. These neutrons can be used to bring about the fission of more atoms (chain reaction).
For nuclear fission to result in a chain rxn the sample must be large enough so that the neutrons are captured internally (too small and neutrons escape). The critical mass for U-235 is 1 to 10 kg.
8 x 107 kJ of energy/ g of 23592U that reacts (equal to 3 x 104 kg of TNT)
Nuclear reactors:
The fuel rods are cylinders that hold enriched (3% U-235) UO2 pellets in zirconium alloy tubes.
The control rods are B or Cd cylinders that absorb neutrons and can control the speed of the rxn.
LWR are moderated by H2O. The water acts as a coolant and slows the neutrons so that the chain rxn continues. HWR use D2O.
The water exiting the reactor is 3200C and is converted to steam at 2700C, which drives the turbogenerator that produces electricity.
Drawbacks – more expensive, nuclear accidents, disposal of waste
Nuclear Fusion
Nuclear fusion is the process by which light nuclei combine with one another to form a heavier nucleus.
Fusion releases more energy than fission.
The light isotopes for fusion are more common than the heavy isotopes need for fission.
Fusion processes have high activation energies (particles have to be accelerated to about 106 m/s to overcome repulsive forces, T = 109 0C).
Containers and collisions with containers are a problem.
In the H-bomb a fission rxn was used to trigger fusion.
Example: deuterium and lithium (low activation E)
21H + 31H --à 42He + 10n
63Li + 10n --à 42He + 31 H
21H + 63 Li --à 2 42He
Solutions – use magnetic fields to confine rxn nuclei, glass pellets with powerful laser
Example
Calculate ΔE, in kilojoules per gram of reactants, in (a) a fusion rxn, 21H + 21H -à 42He (b) a fission rxn, 23592U --à 9038Sr + 14458Ce + 10n + 40-1e. Use published mass values.