Neither natural Uranium nor Plutonium can maintain a chain reaction. ( even small lumps of pure 235U or 239Pu cannot explode simply because of the number of neutrons that escape before inducing fission). Recall we need k = pf(f /total) > 1

A large enough (critical) mass of 235U or 239Pu can chain react with the reaction set off by any accidental initial neutron (even from a rare spontaneous fission event). If N neutrons (initially even 1 or 2) are present at time t their number will increase during the next moment dt by where  is related to k and obviously depends on the fissile material and its geometry. For critical samples of 235U ~108 Hz. As long as we can treat  as a constant where  =1/ is the “generation time.”

Five grades of uranium are commonly recognized: Uranium- 233: fissile, weapon-useable isotope, derived from irradiating 232Th with neutrons, ½ =160,000 years; 10-20 kg required for a nuclear device; less common than U-235 for making nuclear explosives. Uranium-235: best suited for fission bomb (or fast reactor) when enriched to > 90% purity; 6-25 kg required for a nuclear bomb; “significant quantities” standards (for UN inspections) is as little as 3 kg; a recent international study estimates 1,750 tons of highly enriched 235U have been produced worldwide. Five grades of uranium are commonly recognized: 1. Depleted uranium: containing < 0.71% 235U. 2. Natural uranium: containing 0.71% 235U. 3. Low-enriched uranium (LEU), between 0.71 – 20% 235U. commercial power reactors use 2-6 % 235U fuels. cannot be used to make nuclear explosives 4. Highly enriched uranium (HEU): containing > 20% 235U. Research and naval reactors use either LEU or HEU fuel. 5. Weapon-grade uranium: HEU containing > 90% 235U.

best fission explosive nuclear material. Plutonium-239: Highly carcinogenic  ray emitter. Unlike uranium, all (but trace quantities) of Pu are manufactured. 239Pu is produced in nuclear reactors when 238U is irradiated with neutrons. ½ = 24,000 years, and it is a fissile material. Subsequent neutron captures lead to accumulations of 240Pu, 241Pu and 242Pu. 241Pu is fissile, but 240Pu and 242Pu are not. However, all are fissionable by fast neutrons, and can be used either in combination or alone in nuclear explosives; best fission explosive nuclear material. 3-8 kg required for nuclear explosive; "significant quantities standard" 1 kg. The bomb dropped on Nagasaki contained 6.1 kg. There are about 1,200 metric tons of Plutonium on our planet of which some 230 tons have been produced for military purposes. Plutonium is ~10 times more toxic than nerve gas. When inhaled, the smallest particles cause cancer: inhaling 12,000 micrograms (millionths of a gram) causes death within 60 days. The dispersal of 3.5 ounces of plutonium could kill every-one in a large office building. For weapon production, plutonium has to be at least 93% enriched. Plutonium technology for bomb construction is judged to be more difficult than 235U techniques.

The following grades of plutonium are widely used: Weapons can be made out of plutonium with low concentrations of 239Pu and high concentrations of 240Pu, 241Pu, or 242Pu. The plutonium used in nuclear weapons typically contains mostly 239Pu and relatively small fractions of other plutonium isotopes. Plutonium discharged in power reactor fuel typically contains significantly less 239Pu and more of other plutonium isotopes. The following grades of plutonium are widely used: 1. Weapon-grade plutonium: containing < 7% 240Pu. 2. Fuel-grade plutonium: 7 - 18 % 240Pu. 3. Reactor-grade plutonium, containing over 18 percent 240Pu. The term "super-grade plutonium" is sometimes used to describe plutonium containing less than 3 percent plutonium 240. The term "weapon-usable plutonium" is often used to describe plutonium in separated form and, thus able to be quickly turned into weapons components

Before triggering, fissile material is kept in subcritical quantities to prevent accidental explosions. An electrical trigger sets off chemical explosives that drive the subcritical parts together. Active Material each 2/3 critical Propellant Tamper Gun Trigger Assembly Tamper

Enola Gay Little Boy Hiroshima Size: length - 3 meters, diameter - 0.7 meters. Weight: 4 tons. Nuclear material: Uranium 235. Energy released: equivalent to 12.5 kilotons of TNT. Code name:"Little Boy" Hiroshima

released is increasing so rapidly it heats the material to the point Once triggered the chain reaction builds exponentially. Note logarithmic scale! After ~50 generations (0.50 msec) the energy released is increasing so rapidly it heats the material to the point it expands explosively. This scatters the remaining fissile material in subcritical quantities, and the chain reaction ends.

Dropping the first atomic bomb At 2:45am local time (August 6, 1945), the Enola Gay, a B-29 bomber took off from the US air base on Tinian Island in the western Pacific. 6½ hours later, at 8:15 A.M. Japan time, its atomic bomb was dropped and exploded a minute later at an estimated altitude of 58020 meters over central Hiroshima. Initial explosive conditions Maximum temperature at burst point: several million degrees C. A 15m radius fireball formed in 0.1 millisecond, with a temperature of 300,000o C, and expanded to its huge maximum size in one second. The top of the atomic cloud reached an altitude of 17,000 meters. Black rain Radioactive debris fell in a “black rain” for > hour over a wide area.

Damaging effects of the atomic bomb Thermal heat Intense thermal heat emitted by the fireball caused severe burns and loss of eyesight. Thermal burns of bare skin occurred as far as 3.5 kilometers from ground zero (directly below the burst point). Most people exposed to thermal rays within 1-kilometer radius of ground zero died. Tile and glass melted; all combustible materials were consumed. Blast An atomic explosion causes an enormous shock wave followed instantaneously by a rapid expansion of air (the blast); these carry ~half the explosion's released energy. Maximum wind pressure of the blast: 35 tons per square meter. Maximum wind velocity: 440 meters per second. Wooden houses within 2.3 km of ground zero collapsed. Concrete buildings near ground zero (blast from above) had ceilings crushed, windows and doors blown off. Radiation Exposure within 500 meters of ground zero was fatal. People exposed at distances of 3-5 kilometers later showed symptoms of aftereffects, including radiation-induced cancers. Deaths With an uncertain population figure, the death toll could only be estimated. According to data submitted to the United Nations by Hiroshima City in 1976, the death count reached 140,000 (plus or minus 10,000) by the end of December, 1945.

Implosion Assembly Designs Active Material (235U or 239Pu) each 1/3 critical electrical trigger chemical explosive chemical explosive Active Material (235U or 239Pu) subcritical density Implosion Assembly Designs

And left an estimated 70,000 dead by the end of 1945. Fat Man Nagasaki The atomic bomb dropped on Nagasaki exploded at 11:02 A.M. on August 9. Using 6.1 kg of 239Pu it delivered the explosive power of 20 kilotons of TNT-equivalent, And left an estimated 70,000 dead by the end of 1945.