When an atomic bomb explodes, the result is an intense expanding spherical shock wave that propagates out from the source with superheated air behind the expanding shock wave, as seen in the photograph. A very large amount of energy E is generated by nuclear fission at the detonation point. Photograph of an atomic detonation at t = 15 ms (New Mexico, 1945) One of the great fluid dynamicists of the 20th century, G.I. Taylor, used dimensional reasoning to determine the amount of energy released in the detonation shown above. He reasoned that the radius of the blast cloud R depends only upon the density of the air (ρ), the time since the explosion (t), and the energy released (E).

(a) What is your estimate of the energy released in the detonation shown above?

(b) The largest nuclear device ever exploded was the 'Tsar' bomb that was exploded in the atmosphere in 1961 and had a size of 50 Megatons, where 1 Megaton = 4.2 x 10¹⁵ J. The safe distance for an observer was estimated as 45 km. How long did it take the shock wave to reach 'safe' observers? What was the speed of the shock wave when it reached them?