Thursday, August 5, 2010

Remembering Hiroshima and Nagasaki

World War II still remains fresh in our minds, both for the destruction
that was caused worldwide and for all the new innovations it helped
spawning in terms of science and technology. Though these were initially
aimed at giving a strategic military advantage to those countries who
reaped its benefits, in the years that followed after the war, these
innovative ideas have been put to use for more peaceful means. An object
of fascination, dread and ridicule the world over took birth during these
troubled times during which it was also put to use, the atomic bomb. It
brought the end of the war closer when its effects were experienced by the
speechless masses of people in the cities of Hiroshima and Nagasaki in
Japan. The much debated events occurred on 6th August and 9th August, 1945
respectively. By then, Germany had surrendered and Japan was still
battling against the Allied forces. America, which had earlier in 1941
suffered heavy casualties at Pearl Harbor owing to attacks by the Japanese
were prompted to join into the war efforts on a full time basis. They had
been developing the atomic bomb for some time under the Manhattan project
(1942 - 1946) where the research was directed by Robert Oppenheimer.


The “Little Boy” was dropped on 6th August, 1945 on Hiroshima, Japan
making it the first atomic bomb to be used in war. The sustained fission
of Uranium – 235 was used to create a massive explosion at a height of
around 580 m above the city. The mass of the potentially fissile uranium
used was 68 kg of which only 1 kg effectively took part in the fission
reaction. It was estimated that the energy released in the explosion was
roughly 54 TJ, the equivalent of exploding 13 kT (kilo tons) of TNT.
Working backwards using Einstein's mass-energy relation, the amount of
mass that was actually converted into energy turns out to be only 0.6 g
out of the 1 kg of active fissile material.




There were various components that contributed to the destructive power of
the bomb. The initial destruction was in regions close to the explosion
where people present were witness to the high flux of gamma radiation,
neutrons and extreme heat (~ 4000 K) which led to them being instantly
vapourized. This was followed by a blast wave of very high pressure which
coupled with a sufficient time duration of sustenance and a high wind
velocity resulted in the loss of many more lives and destruction on a
massive scale to buildings within a radius of 1.6 km from the blast site.
At a distance of 1.6 km, it was estimated that the pressure would have
been roughly 34 kPa, still enough to cause structural damage to buildings.
Also, the radiation emanating from fissile material that got scattered
would have also contributed to some long term effects in people such as
radiation sickness, cancer, genetic mutations, etc. which have been
studied over the years.

1. Calculate the amount (critical mass) of Uranium-235 that would be required to sustain a chain reaction.
Hint: For the reaction to continue the number of neutrons produced should be more than the number of neutrons captured in the process. Now fission of each Uranium-235 nucleus creates 3 neutrons, a fraction of which is absorbed or lost through the surface. At equilibrium there is a balance between the amount of neutrons produced in the volume and lost through the surface. The actual value of critical mass depends on the geometry and density of the fissile material. For a pure Uranium-235 sample of spherical geometry, the critical mass is about 30 kg. For details of the calculation for critical mass
click here.

2. Calculate the pressure and the radius of shock wave 10 s after the explosion.

3. What would be temperature at the epicentre few milliseconds after the explosion?

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Numerology:

10662526601 is the only known palindromic number whose cube root (2201) is not a palindrome.
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Image courtesy : wikipedia.

1 comment:

  1. Werner Heisenberg, the head of Kaiser Wilhelm Institute, tackled the question of how much uranium 235 (the only isotope of uranium which would work as a nuclear explosive) would be needed to build a bomb and came up with a figure of over a ton - way too high. It is from this mistake that many experts have formed the opinion that Heisenberg did not really understand how a bomb would work. However, Heisenberg corrected his estimate within a few days.

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