Question

How much energy is produced when the sun converts 8 kg into helium and energy?(hint: how does this problem differ from when the sun converts 8 kg of mass into energy)

Answer 1

Solution:-Since 1 gram of hydrogen atoms is equal to its one mole.

So number of moles in 8kg(8000 gram)=8000 moles

No. of atoms per mole=Avagadro number=6.022x10²³

So total number of hydrogen atoms in 8kg i.e. in 8000 moles=8000x6.022x10²³

                                                                                       =4.8176x10²⁷

Since during nuclear fusion inside the sun four Hydrogen atoms convert into single He atom and energy released due to mass difference between reactants and product masses.

So number of He atoms form by such number of hydrogen atoms

                                       

                                     

Mass of 1 hydrogen atlom=1.00794 AMU

so mass of 4 hydrogen atoms=4x1.00794=4.03176 AMU

now mass of 1 He atom =4.002602 AMU

So mass reduction when 4 hydrogen is converted into 1 helium

                           =4.03176-4.002602

                           =0.029158 AMU

Since number of He atom formed by 8 kg hydrogen is 1.2044x10²⁷

So total mass reduction=0.029158 x1.2044x10²⁷

                                         =3.51179x10²⁵ AMU

                                  =3.51179x10²⁵x1.66x10^-27Kg

                                 =5.82957x10^-2Kg

Now released energy

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Now if 8kg mass directly converted into energy then amount of energy released-