Alpha Decay and the mass defect

On this and other pages I will be using atomic mass units u as my unit of mass. 
A carbon 12 atom has, by definition, a mass of 12u so 1u = 1.0 x 10^-3 / 6.02 x 10²³ ( as 1 mole of Carbon 12 is 12.0g ) = 1.66 x 10^-27 kg

Atomic mass units are very useful when we are dealing with very small masses.

Consider a typical alpha decay, that of Radium 226. The alpha particle is emitted with an energy of 4.87MeV

We know the mass of these particles very accurately from mass spectrometry.  See this amazing web site

Lets consider the mass on both sides of the equation

( note - the actual masses are slightly different on after as I have not taken electrons into account, but the total mass is accurate)

The total mass after = 226.02017u   It appears that we have lost some mass, approximately 0.0052u. Where has it gone?

You may have heard that mass and energy are interchangeable. Perhaps this mass has changed into energy?

Using E = m c² this much mass is equivalent to 0.0052 x 1.66 x 10^-27 x ( 3 x 10⁸ )² = 7.77 x 10^-13J = 4.86 MeV