Distance of Closest Approach
For a head-on approach to a heavy stationary nucleus, the alpha particle's kinetic energy at large separation equals the Coulomb potential energy at the classical turning point. Nuclear recoil is neglected unless the problem supplies finite target mass.
Why this shows up in the exam
Estimating nuclear-size upper bounds · Comparing projectiles of different energies · Finding beam speed from closest approach
Learn the idea
In a head-on alpha collision, initial kinetic energy becomes electrostatic potential energy at the turning point. A head-on alpha particle climbs an electrostatic hill. It stops momentarily at the closest point, so energy conservation fixes that distance without needing the detailed trajectory.
🧠 Memory hook: At the turning point, speed is zero and Coulomb energy owns the budget.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- K = (1/(4 pi epsilon₀)) (2 Z e²)/r_min — head-on closest approach to a nucleus of atomic number Z
- r_min proportional to Z/K — scaling at fixed projectile charge
How to approach it
- 1Convert MeV to joules only if using SI constants
- 2Set initial kinetic energy equal to Coulomb potential
- 3Check that the result is on a femtometre scale
Common slip-ups that cost marks
- •Using the atomic radius as r_min
- •Forgetting the alpha charge is +2e
- •Applying the head-on result to arbitrary impact parameter
🌟 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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