a plutonium bomb was tested in new mexico in 1945, approximately 1 gram of matter was converted into energy,?

E = mc^2

If the mass defect was 1 gram, then:

E = (0.001kg)(299,792,458m/s) (299,792,458m/s) (1GigaJoule/10^9kg.m^2/s^2) = 89,875.5 GigaJoules

That's about 24.96 Gigawatt-hours. Enough to power a city for a couple of days.

Well, this makes me feel old.

While I was not around in 1945, I do know there weren't pocket electronic calculators back then (and any I am old enough to remember slide rules) back in 1945 if you asked some one this question they would have noticed the "approximately" since back then squaring 299 792 458 would have been a lot more work than squaring 3*10^8; (= 9 * 10^16, pretty simple) then 9*10^16 * 1*10^-3 = 9*10^13 Actually even using a calculator, squaring "3*10^8" would be 5 keystrokes for 3*10^8; 3, "x10^x" (or whatever the key is on your calculator) , 8 , X² , = ; compared to 11 for the more precise version of c

While going from "approximately 1" to 4, 6 or 10 significant figures would be typical here on Y!A, I'd say map's answer is the best, though Jack's comparison to powering a city was useful.

e=mc^2

The speed of light is actually 299792458 m/s so I got 8.987551787*10^13 joules. But since the amount of matter converted was aproximately 1 gram any aproximation of the speed of light will do as long as it is in the neighbourhood of 3*10^8 m/s.

Use above answers, or mine, to compare with TNT which detonates with an energy of 1360 joules per gram. How many kilotonnes of TNT did the bomb compare with?

Tinkertailor:

Scary what wrong calcualtions can do in situation like those. Like you said they didn´t have calculators back then. They did have the first "electronic brains" but calculations went wrong anyway. Like when the US tested one of the earlier H bombs in the pacific and the thing detonated with a force ten times greater than what was expected. A japanese fishing boat was hit and the crew radiation posioned because someone forgot to carry the one...

E = m c^2 = 0.001 * (300000000)^2 Joule = 9 * 10^13 Joule