Einstein's Theory of Relativity         

    Nuclear reactions are accompanied by small losses in mass. These small amounts of mass are not really lost, they are converted into energy, as described in the relationship

E = mc²

 E = the amount of energy released, in Joules
 m = the amount of mass lost, in kilograms
c² = the speed of light squared (a constant value equal to 9.00 x 10¹⁶ m²/s²)*

  *Even though the amount of mass lost  in a nuclear reaction is very small, the amount of energy released is huge because the value of c² is very large.

 
Solving this equation:

   First, write out the balanced nuclear reaction for the decay process that has occurred.                              
                                    example:  ₈₈Ra²²⁶ →  ₈₆Rn²²²   +  ₂He⁴  

   Next, determine the change in mass that occurred during the transmutation of elements.

Dm = (mass of products - mass of reactants)
Dm = (mass of ₈₆Rn²²²   +  ₂He⁴  -  ₈₈Ra²²⁶
Dm = (221.970 3 +  4.001 50) - (225.977 1) x 10^-3 kg/mol
(above values found on page 8 of your data booklet)
Dm = (-0.005 3) x 10^-3 kg/mol
(a small negative value because a small amount of
mass was lost during the alpha decay reaction)
Dm = -5.3 x 10^-6 kg/mol
(convert to proper scientific notation)

     Finally, substitute this value into the E = mc² equation and solve it:

E = mc²
E = -5.3 x 10^-6 kg/mol x 9.00 x 10¹⁶ m²/s²
E = -4.8 x 10¹¹ J/mol (since 1 J = 1 kg^.m²/s²)
 

   If you are asked to solve for the amount of energy produced per kilogram of parent material, simply divide the answer for E = mc² above by the mass of the parent material given.
In this example, the answer would be:
E (J/kg) = (-4.8 x 10¹¹ J/mol)/(225.977 1 x 10^-3 kg/mol)
E  = -2.1 x 10¹² J/kg