A simple conversion question that im getting wrong

[nemzy]

I am confused why i am not getting this one right..


The energy associated with the atomic bomb explosion over Hiroshima was equivalent to 13 kilotons of TNT. To how many "Hiroshima Bombs" would the metoerite impact have been equivalent?

A meteorite impact has a kinetic energy of 4.5e14

1 atomic bomb = 13 kilotons of TNT

and 1 megaton of TNT = 4.2e15

answer:

this is how i did it..

(4.2e15 megaton)(10^6 ton/1megaton)(1 kiloton/1000 ton)= 4.2e18

(4.2e18 kiloton)(13)=5.46e19

so..4.5e14/5.46e19 =8.24e-6 which is NOT the right answer?

where did i make my mistake? thanks

 

[NateTG]

The problem asks for the number of Hiroshima bombs, not the energy so you should probably do something like:

1Meteorit * \frac{4.5 * 10^{14} J}{1 Meteorite}*\frac{1 MT}{4.2 * 10^{15} J} * \frac{1000 KT}{1 MT} * \frac{1 Nuke}{13 KT}

Note that the unit on the bottom is on the top in the previous term. As long as you make sure that each of the fractions is equal to 1, you should be OK using this method.

The mistake that you're making is that you're not being careful with your units. For example, in the first product you've got "(4.2e15 megaton)" when it really should be "1 Megaton/4.2e15" or "4.2e15/Megaton" it woud be good to keep the 'J' or whatever units of energy you're using.

Because you're not keeping good track of the units, it's hard to tell whether the results that you're getting are being combined correctly.

You should, for example, be getting that a Kilonton is 1/1000th of a Megaton - so 1 Kiloton TNT = 4.2e12 J and 1 nuke = 13 Kilotons TNT = 5.4 e 13 J. You got some different numbers.

 

[M98Ranger]

It looks like you made a mistake in converting from megatons to kilotons. Here is the correct conversion:

1 megaton = 1,000 kilotons

So, the correct calculation would be:

(4.5e14 megaton)(1,000 kiloton/1 megaton)(1 atomic bomb/13 kilotons) = 3.46e12 atomic bombs

This means that the meteorite impact would have been equivalent to approximately 3.46 trillion atomic bombs, which is a huge amount of energy! Keep in mind that this is just an estimate and the actual energy released by the impact may vary. Hope this helps!