Question

The total annual energy consumption in the U.S.A. is 1.00 x 1020 joules. If you were capable of converting mass to energy with 100% efficiency, how much mass, in kg, would you need to produce an energy E = 1 x 1020 joules?

A) 1.11 x 104 kg
B) 3.00 x 1028 kg
C) 3.33 x 1011 kg
D) 9.00 x 1036 kg

Answer 1

See answer below

Step-by-step explanation:

Hi there,

To get started, use the famous equation that purely relates energy and mass,

`E = mc^(2)` where c is the speed of light, a constant: 2.99792458
`* 10^8` m/s

and m is mass in kilograms. Note, majority of physics equations only work if in SI units, though there are exceptions.

Since we are asked for mass, solve for m:

`m = (E)/(c^(2) )`
`= (1.00*10^(20) \ J )/((2.99792458*10^8 \ m/s)^2) = 1.11*10^3 \ kg`

So, option A is correct. However, I believe you have a typo in Option A as it should be x10^3 not x10^4, or a typo somewhere else in the x10 powers.

Thanks,