The russians detonated the largest bomb to date in 1961, a thermonuclear (hydrogen bomb) weighing in at 27 tonnes, with the explosive power of 50Mt or 50,000,000 tonnes of TNT. It sent a shock wave measuring a 5 on the Richter scale, still being detectable after travelling three times around the earth. This explosion blew a mushroom cloud approx 40 miles from the earths surface. It is rather more difficult to define exactly where the borderline between the atmosphere and outerspace lies. There is a boundery at an altitude of 62 miles called the Karmen line which was understood to be the cutoff point between our atmosphere and space. This altitude was calculated from the gradual decreasing pressure and the increased velocity required for a craft to maintain a steady altitude. These calculations are far from precise with a large margin for error. To be more truthful there is not as I understand it a clear cut definition of where earths atmosphere ends and space begins. So to answer your question as best as I am able, if it were possible to send a mushroom cloud into space, you would need a very substantial bomb. For the cloud to escape the earths atmosphere and gravitaional influences would require enormous amounts of energy.