A “ton of TNT” is defined as 4.184 x 109 J 1 kg = 2.205 lb 1 J = 1 N-m = 1 kg-m2

Question

A “ton of TNT” is defined as 4.184 x 109 J 1 kg = 2.205 lb
1 J = 1 N-m = 1 kg-m2/s2
1 calorie = 4.184 J

1 u = 1.6605 x 10-27 kg
c (Speed of light) = 2.998 x 108 m/s

1) A hydrogen nucleus (proton) has a mass of 1.00783 u.

If a proton could be converted into energy, how much would be produced?

A calorie is the amount of heat that can raise the temperature of water by 1°C. How many protons would it take to raise water from 0° - 100°C?

How much H does this represent (in g).

2) Consider the uranium atomic bomb dropped on 6 August 1945. It used 142 lbs of 235U, and the yield was 12.5 kilotons. What fraction of the 235U mass was converted to energy in the explosion?

Explanation / Answer

Mass of hydrogen nucleus m = 1.00783 u

                                           = 1.00783 x 1.6605 x10 -27 kg

We know according to mass energy relation E = mc 2

Where c = Speed of light = 3 x10 8 m/s

E = ( 1.00783 x 1.6605 x10 -27 )(3x10 8 ) 2

      = 1.506 x10 -10 J

      = [(1.506 x10 -10 )/4.186] cal

      = 3.597 x10 -11 Cal

Heat required to raise the water from 0 o C to 100 oC is = 100 cal

Number of proton N = 100 /(3.597 x10 -11 )

                             = 2.779 x10 12

Mass of 6.023 x10 23 hydrogen = 1 g

So, mass of ( 2.779 x10 12 ) hydrogen = ( 2.779 x10 12 )(1 g) /(6.023 x10 23)

                                                        = 4.614x10 -12 g

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