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Find the mass converted into energy by a 12.0-kT bomb. a) 2.15×10⁹ kg b) 3.75×10⁹kg c) 5.62×10⁹kg. d) 7.50×10⁹kg

User Adamjansch
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1 Answer

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Final answer:

The mass converted into energy by a 12.0-kT bomb is calculated using Einstein's mass-energy equivalence formula, E=mc², and yields a mass of approximately 5.58×10⁲ kg, which is not provided in the given options.

Step-by-step explanation:

To find the mass converted into energy by a 12.0-kT (kiloton) bomb, we use the mass-energy equivalence formula derived from Einstein's theory of relativity, E=mc², where E is energy, m is mass, and c is the speed of light in a vacuum (approximately 3.00×10⁸ m/s).

First, we must convert kilotons to joules, recognizing that 1 kiloton of TNT is equivalent to 4.184×10¹² joules. Therefore, the energy released by a 12.0-kT bomb is 12.0×10³ kilotons × 4.184×10¹² joules/kiloton = 5.0208×10¹⁴ joules.

Applying the mass-energy equivalence formula, we have m = E / c² = 5.0208×10¹⁴ J / (3.00×10⁸ m/s)², which simplifies to approximately 5.58×10⁲ kg. So, none of the given options are correct, assuming the stated values are the only possible answers.

User Gcali
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