Nuclear Reaction Balancing and Q Value
For a reaction a + A -> b + B, nucleon number and electric charge are conserved, as are total energy and vector momentum. The reaction value is Q = (sum initial rest masses - sum final rest masses)c^2.
Why this shows up in the exam
Finding missing reaction products · Testing whether a proposed decay is energetically allowed · Calculating reaction energy from masses
Learn the idea
A valid nuclear equation conserves charge, baryon count, energy, and momentum, while Q records the rest-energy change. Balance A and Z first to identify missing particles. Then compare initial and final rest masses: lost rest mass appears as kinetic or photon energy, while gained rest mass requires supplied energy.
🧠 Memory hook: Balance A and Z, then let mass decide Q.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum A_initial = sum A_final — baryon or nucleon-number balance for ordinary nuclear reactions
- sum Z_initial = sum Z_final — electric-charge balance
- Q = (m_initial - m_final)c² — positive Q is exothermic; negative Q is endothermic
How to approach it
- 1Make separate A and Z balance columns
- 2Use a consistent atomic- or nuclear-mass convention
- 3Check momentum as well as the mass-energy ledger
Common slip-ups that cost marks
- •Balancing A but not Z
- •Assuming conservation laws make every reaction energetically possible
- •Reversing the sign of Q
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In hydrogen, an electron transitions from n = 2 to n = 1. Using E_n = -13.6/n^2 eV, find the emitted photon energy.
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