Energy released in radioactive decay
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Flip to reveal answersWhat is the 'mass defect' in a nuclear decay?
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Question
What is the 'mass defect' in a nuclear decay?
Answer
How much **lighter** the products are than the parent nucleus: Δm = parent mass − total product mass.
Question
What is the 'released energy' (disintegration energy Q)?
Answer
The energy the **mass defect** turns into, shared as kinetic energy of the products. Found from E = mc².
Question
Which equation links the mass defect to the released energy?
Answer
$E = mc^{2}$ — mass-energy equivalence (given in the data booklet). Here m is the mass defect.
Question
Fast way to convert a mass defect in u into energy in MeV?
Answer
Multiply Δm (in u) by **931.5**, because 1 u = 931.5 MeV c⁻².
Question
Why must you keep all decimal places when finding a mass defect?
Answer
The defect is a **tiny** difference of large numbers — rounding early loses the answer entirely.
Question
After a decay from rest, how do the two products' momenta compare?
Answer
**Equal and opposite** (same size p), so the total momentum stays zero — conservation of momentum.
Question
Why does the lighter product carry most of the energy?
Answer
Same momentum p, and KE = p²/2m, so the **smaller** mass gives the **bigger** kinetic energy.
Question
Energy-share ratio between the two decay products?
Answer
KE_{alpha} : KE_{daughter} = m_{daughter} : m_{alpha}. The alpha's share = m_{daughter} ÷ (m_{daughter} + m_{alpha}).
Question
In an alpha decay of a heavy nucleus, roughly what fraction of the energy does the alpha get?
Answer
Almost all of it — around **98%** — because the heavy daughter barely recoils.
Question
A decay has Δm = 0.0052 u. Energy released in MeV?
Answer
E = 0.0052 × 931.5 ≈ **4.8 MeV** (about 5 MeV).
Question
Three-step routine for a decay-energy question?
Answer
1) mass defect Δm = parent − products; 2) E = mc² (or Δm × 931.5 for MeV); 3) the light product carries most of the energy.
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Radioactive decay
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