For the hydrogen bomb reaction to become self-sustaining, a so-called critical temperature of about 3.5 × 107 K (6.3 × 107°F) must be attained with the aid of the enormous temperature created by a fission explosive. Once this temperature is achieved, the energy released in the initial reaction maintains the temperature, and the chain proceeds either until the supply of fusionable material is exhausted or until sufficient expansion has taken place that the material is cooled below the critical temperature.
There are two ways to use fusion:
boosting of fission explosive yields or generating multistage thermonuclear reactions.
In a fusion-boosted warhead, when the sphere of fissile materials is compressed (imploded) by the chemical explosion, an uncontrolled fission chain reaction begins. If there is fusionable material inside the device, thermonuclear reactions will boost the fission yield. The fusion reactions do not directly contribute very much to the explosive energy, but instead enhance the fission rate, due to the release of a large number of additional neutrons.
If the massive casing is made mostly of uranium-238 (natural or depleted uranium), neutrons from the thermonuclear reactions will cause the uranium nuclei to undergo fission, giving off still more energy. A device of this sort can be regarded as a three-stage fission-fusion-fission bomb.
The yield, or total energy, of a hydrogen bomb is expressed in megatons (1 megaton equals 1015 calories or 4.18 × 1015 joules). Typical fusion-boosted weapons yield hundreds of kilotons (tenths of megatons), and typical multistage weapons yield megatons.
NUCLEAR WEAPONS
Nuclear weapons derive their explosive power from the fission (splitting) and fusion (combining) of atoms. Fusion devices need to be combined with a nuclear fission weapon to generate the intense heat necessary to begin the still more powerful process of fusion. Fusion weapons—the ‘H’ (hydrogen) bomb—can be a thousand times more powerful than fission weapons and these opened the horrific possibility of glob
al destruction through nuclear missile war. Many early ‘fusion’ weapons were in fact ‘boosted fission devices’, gaining most of their power from the fission explosion with a fusion component to enhance its efficiency. Military requirements have also led to enhanced radiation/reduced blast weapons, the so-called ‘neutron bomb’, in which the immediate radiation is multiplied in order to kill troops rather than destroy installations.
The idea of a source of enormous e
nergy for motive power or weapons featured in the work of 19th-century science-fiction writers including Jules Verne, George Earle Bulwer-Lytton, and H. G. Wells who talks of atomic bombs in The World Set Free. By 1914 the Newtonian view that the universe consisted of lumps of indestructible matte
r had given way to the realization that matter could be transformed into energy.
It was not until the eve of WW II that the practical possibility of a nuclear weapon was understood. On 2 August 1939, Albert Einstein signed a letter to Pres Franklin D. Roosevelt, saying that recent work in France and the USA had indicated the possibility of setting up a nuclear chain reaction in a large mass of uranium. This new phenomenon could ‘also lead to the construction of bombs and it is conceivable—though much less certain—that extremely powerful bombs of a new type may thus be constructed. A single bomb of this type, carried by boat and exploded in a port, might very well destroy the whole port, together with some of the surrounding territory. However, such bombs might very well prove too heavy for transportation by air.’ He was wrong on the last point, and six years and four days later the US dropped the first atomic bomb over Hiroshima, the result of the Manhattan Project.
The first test bomb ever to be exploded, at Alamogordo in the New Mexico desert on 16 July 1945, ‘the Gadget’, was an ‘implosion’ device, with a hollow plutonium core weighing about 8.3 lb (3.8 kg), compressed to critical density by about 4, 866 lb (2, 270 kg) of high explosive. The ‘yield’—the size of the explosion—was 22 kilotons. Nuclear weapon yields are measured as kilotons (each 1, 000 tons of TNT) or megaton
s (one million tons of TNT).
The first bomb to be dropped on Japan on 6 August was of a different type—a ‘gun-assembly’ device called ‘Little Boy’. It was cruder than the Gadget—132.3 lb (60 kg) of highly enriched uranium in two pieces, one of which was fired at the other down a gun-type barrel, producing a far less efficient yield of 12 to 15 kilotons. The US B-29 bomber Enola Gay, named after the pilot's mother, carried the bomb to Hiroshima from its base at Guam, escorted by two other planes carrying observers and instruments. The bomb had been brought from the USA by the cruiserIndianapolis, which was to be sunk by a Japanese submarine on its return trip. The city was obliterated.
Molecular Orbital Theory
O2 O
Each line in the molecular orbital diagram represents a molecular orbital, which is the volume within which a high percentage of the negative charge generated by the electron is found. The molecular orbital volume encompasses the whole molecule. We assume that the electrons would fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms.
The molecular orbitals are filled in a way that yields the lowest potential energy for the molecule.
The maximum number of electrons in each molecular orbital is two. (We follow the Pauli exclusion principle.)
Orbitals of equal energy are half filled with parallel spin before they begin to pair up. (We follow Hund's Rule.)
Before we continue with a description of a model used to generate molecular orbital diagrams, lets get a review of light and electron waves and how two waves can interact. The wave description of light describes the effect that the light has on the space around it. This effect is to generate an oscillating electric and magnetic fields. These fields can vary in intensity, which is reflected in varying brightness of light.
The wave description of the electron describes the variation in the intensity of negative charge generated by the electron.
Light waves can interact in-phase, which leads to an increase in the intensity of the light (brighter) and out-of-phase, which leads to a decrease in the intensity of the light (less bright). Electron waves can also interact in-phase and out-of-phase. In-phase interaction leads to an increase in the intensity of the negative charge. Out-of-phase interaction leads to a decrease in the intensity of the negative charge.
One common approximation that allows us to generate molecular orbital diagrams for some small diatomic molecules is called the Linear Combination of Atomic Orbitals (LCAO) approach. The following assumptions lie at the core of this model.
Molecular orbitals are formed from the overlap of atomic orbitals.
Only atomic orbitals of about the same energy interact to a significant degree.
When two atomic orbitals overlap, they interact in two extreme ways to form two molecular orbitals, a bonding molecular orbital and an antibonding molecular orbital.
For example, our model assumes that two 1s atomic orbitals can overlap in two extreme ways to form two molecular orbitals. One of the ways the atomic orbitals interact is in-phase, which leads to wave enhancement similar to the enhancement of two in-phase light waves. Where the atomic orbitals overlap, the in-phase interaction leads to an increase in the intensity of the negative charge in the region where they overlap. This creates an increase in negative charge between the nuclei and an increase in the plus-minus attraction between the electron charge and the nuclei for the atoms in the bond. The greater attraction leads to lower potential energy. Because electrons in the molecular orbital are lower potential energy than in separate atomic orbitals, energy would be required to shift the electrons back into the 1s orbitals of separate atoms. This keeps the atoms together in the molecule, so we call this orbital a bonding molecular orbital. The molecular orbital formed is symmetrical about the axis of the bond. Symmetrical molecular orbitals are called sigma, σ, molecular orbitals. The symbol σ1s is used to describe the bonding molecular orbital formed from two 1s atomic orbitals.
The second way that two atomic orbitals interact is out-of-phase. Where the atomic orbitals overlap, the out-of-phase interaction leads to a decrease in the intensity of the negative charge. This creates a decrease in negative charge between the nuclei and a decrease in the plus-minus attraction between the electron charge and the nuclei for the atoms in the bond. The lesser attraction leads to higher potential energy. The electrons are more stable in the 1s atomic orbitals of separate atoms, so electrons in this type of molecular orbital destabilize the bond between atoms. We call molecular orbitals of this type antibonding molecular orbitals. The molecular orbital formed is symmetrical about the axis of the bond, so it is a sigma molecular orbital with a symbol of σ*1s. The asterisk indicates an antibonding molecular orbital.
The following diagram shows the bonding and antibonding molecular orbitals formed from the interaction of two 1s atomic orbitals.
When two larger atoms atoms combine to form a diatomic molecule (like O2, F2, or Ne2), more atomic orbitals interact. The LCAO approximation assumes that only the atomic orbitals of about the same energy interact. For O2, F2, or Ne2, the orbital energies are different enough so only orbitals of the sameenergy interact to a significant degree.
Like for hydrogen, the 1s from one atom overlaps the 1s from the other atom to form a σ1s bonding molecular orbital and a σ*1s antibonding molecular orbital. The shapes would be similar to those formed from the 1s orbitals for hydrogen. The 2s atomic orbital from one atom overlaps the 2s from the other atom to form a σ2s bonding molecular orbital and a σ*2s antibonding molecular orbital. The shapes of these molecular orbitals would be similar to those for the σ1s and σ*1s molecular orbitals. Both σ2s and σ*2s molecular orbitals are higher energy and larger than the σ1s and σ*1s molecular orbitals.
The p atomic orbitals of the two atoms can interact in two different ways, parallel or end-on. The molecular orbitals are different for each type of interaction. The end-on interaction between two 2px atomic orbitals yields sigma molecular orbitals, which are symmetrical about the axis of the bond.
The two 2py atomic orbitals overlap in parallel and form two pi molecular orbitals. Pi molecular orbitals are asymmetrical about the axis of the bond.
The 2pz-2pz overlap generates another pair of π2p and π*2p molecular orbitals. The 2pz-2pz overlap is similar to the The 2py-2py overlap. To visualize this overlap, picture all of the orbitals in the image above rotated 90 degrees so the axes that run through the atomic and molecular orbitals are perpendicular to the screen (paper). The molecular orbitals formed have the same potential energies as the molecular orbitals formed from the 2py-2pyoverlap.
There is less overlap for the parallel atomic orbitals. When the interaction is in-phase, less overlap leads to less electron charge enhancement between the nuclei. This leads to less electron charge between the nuclei for the pi bonding molecular orbital than for the sigma bonding molecular orbital. Less electron character between the nuclei means less plus-minus attraction, less stabilization, and higher potential energy for the pi bonding molecular orbital compared to the sigma bonding molecular orbital.
When the interaction is out-of-phase, less overlap leads to less shift of electron charge from between the nuclei. This leads to more electron charge between the nuclei for the pi antibonding molecular orbital than for the sigma antibonding molecular orbital. More electron charge between the nuclei means more plus-minus attraction and lower potential energy for the pi antibonding molecular orbital compared to the sigma antibonding molecular orbital.
The expected molecular orbital diagram from the overlap of 1s, 2s and 2p atomic orbitals is as follows. We will use this diagram to describe O2, F2, Ne2, CO, and NO.
We use the following procedure when drawing molecular orbital diagrams.
Determine the number of electrons in the molecule. We get the number of electrons per atom from their atomic number on the periodic table. (Remember to determine the total number of electrons, not just the valence electrons.)
Fill the molecular orbitals from bottom to top until all the electrons are added. Describe the electrons with arrows. Put two arrows in each molecular orbital, with the first arrow pointing up and the second pointing down.
Orbitals of equal energy are half filled with parallel spin before they begin to pair up.
We describe the stability of the molecule with bond order.
bond order = 1/2 (#e- in bonding MO's - #e- in antibonding MO's)
We use bond orders to predict the stability of molecules.
If the bond order for a molecule is equal to zero, the molecule is unstable.
A bond order of greater than zero suggests a stable molecule.
The higher the bond order is, the more stable the bond.
We can use the molecular orbital diagram to predict whether the molecule is paramagnetic or diamagnetic. If all the electrons are paired, the molecule is diamagnetic. If one or more electrons are unpaired, the molecule is paramagnetic.
EXAMPLES:
1. The molecular orbital diagram for a diatomic hydrogen molecule, H2, is
The bond order is 1. Bond Order = 1/2(2 - 0) = 1
The bond order above zero suggests that H2 is stable.
Because there are no unpaired electrons, H2 is diamagnetic.
2. The molecular orbital diagram for a diatomic helium molecule, He2, shows the following.
The bond order is 0 for He2. Bond Order = 1/2(2 - 2) = 0
The zero bond order for He2 suggests that He2 is unstable.
If He2 did form, it would be diamagnetic.
3. The molecular orbital diagram for a diatomic oxygen molecule, O2, is
O2 has a bond order of 2. Bond Order = 1/2(10 - 6) = 2
The bond order of two suggests that the oxygen molecule is stable.
The two unpaired electrons show that O2 is paramagnetic.
4. The molecular orbital diagram for a diatomic fluorine molecule, F2, is
F2 has a bond order of 1. Bond Order = 1/2(10 - 8) = 1
The bond order of one suggests that the fluorine molecule is stable.
Because all of the electrons are paired, F2 is diamagnetic.
5. The molecular orbital diagram for a diatomic neon molecule, Ne2, is
Ne2 has a bond order of 0. Bond Order = 1/2(10 - 10) = 0
The zero bond order for Ne2 suggests that Ne2 is unstable.
If Ne2 did form, it would be diamagnetic.
We can describe diatomic molecules composed of atoms of different elements in a similar way. The bond between the carbon and oxygen in carbon monoxide is very strong despite what looks like a strange and perhaps unstable Lewis Structure.
The plus formal charge on the more electronegative oxygen and the minus formal charge on the less electronegative carbon would suggest instability. The molecular orbital diagram predicts CO to be very stable with a bond order of three.
We predict the nitrogen monoxide molecule to be unstable according to the Lewis approach to bonding.
The unpaired electron and the lack of an octet of electrons around nitrogen would suggest an unstable molecule. NO is actually quite stable. The molecular orbital diagram predicts this by showing the molecule to have a bond order of 2.5.
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