Compute the total possible energy released from an annihilation of x-grams of anti-matter and the same quantity of matter, where x is the last two digits of your SS# or DL#. (20 points) –Use the famous Einstein’s formula for mass-energy equivalence •Compute the power output of this annihilation when the energy is released in x ns, where x is again the first two digits of your SS# or DL#. (10 points) •Compute how many cups of gasoline (8MJ) this energy corresponds to. (5 points) •Compute how many months of world electricity usage (3.6GJ/mo) this energy corresponds to. (5 points)

i)  8.82 * 10^15 J

ii) 1.8 * 10^23 watts

iii) 1.102 * 10^9 number of cups

iv) 2.450 * 10^6  number of months

Explanation:

i)Total possible energy released

Mtotal = x + x

          = 2x * 10 ^-3 kg

when we apply the famous Einstein's formula for mass-energy equivalence

E = Mtotal * c^2

c = speed of light in free space = 3 * 10^8 m/s^-1

x = 49 g

therefore the Total energy released

E = ( 2 * 49 * 10^-3 ) * ( 3* 10^8 ) ^2  =  8.82 * 10^15 J

ii) power output

x in ns = 49 * 10^-9 s

therefore energy released per sec = Total energy released / 49 * 10^-9

= (8.82 * 10^15 ) / ( 49 * 10^-9 ) = 1.8 * 10^23 J

hence power output = 1.8 * 10^23 J  * s^-1  = 1.8 * 10^23 watts

iii) Calculate the number of cups

Total energy obtained in a cup  = 8 MJ = 8* 10^6 J

number of cups required to match of the Total energy released

n = Total energy released / energy obtained in a cup

  = ( 8.82 * 10^15 ) / ( 8 * 10^6 ) = 1.102 * 10^9 number of cups

iv) Calculate the number of months

n = Total energy released / energy obtained in a month

  = (8.82 * 10^15 ) / ( 3.6 * 10^9) = 2.450 * 10^6  number of months

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