Chemistry - Decay scheme of sodium-24

For energy levels in nuclei (and their gamma emission) the first place to look is at the Evaluated Nuclear Structure Data Files. I usually use the Brookhaven site, but there may be a closer mirror to you. Enter 24 into the Nuclide or Mass box and hit Enter. Check the 'Adopted Levels, Gamma' box by $^{24}$Mg, and request the pdf version (back up at the top).

On the last page you will find the lower levels like this (although rotated by 90 degrees):

24Mg gamma levels

So, the 4122.889 keV level has a decay time of 22 fs - this is the level that the first gamma decays from. The 1368.672 keV level has a decay time of 1.33 ps - this is the second gamma in your sequence.