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If a nanogram ($$10^{-9}\text{ g}$$) of mass were to be completely converted into electrical energy and used to power a $$40\text{ W}$$ lamp, find the time (in seconds) for which the lamp can be run. Assume the mass is converted at a uniform rate to produce the power required by the lamp.
Correct Answer: 2250
$$E = mc^2 = 10^{-12}\text{ kg} \times (3 \times 10^8)^2 = 9 \times 10^4\text{ J}$$. The lamp uses $$40\text{ J}$$ each second, so it runs for $$\frac{9 \times 10^4}{40} = 2250\text{ s}$$, i.e. 37.5 minutes.
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