Nuclear Radius and Geometric Scaling
The empirical radius of a roughly spherical nucleus is R = R0 A^(1/3), with R0 about 1.2 fm. Ratios are more reliable than inserting a rounded R0, and the model describes bulk size rather than detailed nuclear shape.
Why this shows up in the exam
Comparing nuclear radii · Finding surface-area changes · Combining momentum ratios with fragment sizes
Learn the idea
Nuclear radius grows as A^(1/3), so area grows as A^(2/3) and volume grows as A. Nucleons pack with nearly constant spacing. Adding nucleons therefore increases volume almost in proportion to their number, while radius increases only as the cube root of that number.
🧠 Memory hook: Radius takes the cube root; area takes two thirds.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- R = R0 A^(1/3) — empirical nuclear-radius law for a roughly spherical nucleus
- R1/R2 = (A1/A2)^(1/3) — radius ratio when the same radius constant is applicable
- S proportional to A^(2/3) — surface-area scaling for spherical nuclei
How to approach it
- 1Form a ratio before inserting R0
- 2Cube a radius ratio to obtain a mass-number ratio
- 3State the spherical bulk-radius assumption
Common slip-ups that cost marks
- •Using R proportional to A
- •Applying the cube root to surface area
- •Mixing femtometres and metres in numerical work
🌟 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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