Nuclear fission and Q-values

Key ideas

• Nuclear fission is the splitting of a large, heavy nucleus into two smaller nuclei (plus usually some free neutrons), releasing energy.
• Fission releases energy because the total mass after the reaction is less than the total mass before — by $E = mc^2$, this "missing" mass reappears as energy, mostly as the kinetic energy of the fragments.
• The energy released in any nuclear reaction is called the Q-value:

$Q = \Delta m \, c^2 = (m_{before} - m_{after})c^2$

• Each variable, with sub-bullets:
  • $Q$ — the energy released by the reaction (J, or MeV using $1$ u $= 931.5$ MeV/c²)
  • $m_{before}$ — total mass of everything entering the reaction (u or kg)
  • $m_{after}$ — total mass of everything produced by the reaction (u or kg)
  • a positive $Q$ means energy is released (mass decreases); this is what makes a reaction happen spontaneously or usefully in a reactor.
• A typical fission reaction: a heavy nucleus such as uranium-235 absorbs a neutron, becomes unstable, and splits — e.g. into barium and krypton isotopes, plus several free neutrons.
• Those released neutrons can go on to trigger fission in further U-235 nuclei — a chain reaction — which is what makes controlled fission useful for power generation (and uncontrolled fission destructive in a weapon).

Tips

• State explicitly that the "missing" mass becomes kinetic energy of the products, via $E = mc^2$ — simply calculating $Q$ without this explanation misses the physics marks in longer-answer questions.
• Fission Q-value questions often supply masses for every particle on both sides (including free neutrons) — total them carefully; forgetting a neutron on either side is the most common arithmetic slip.