Confining a Gamma-Ray Photon to Nuclear Scale
1 · Predict
If you tried to confine a photon to within a single atomic nucleus (about a femtometre across), the uncertainty principle demands an enormous minimum momentum uncertainty. Does this help explain why free electrons are never found INSIDE a nucleus?
- Yes — confining any light particle to nuclear scale would require momentum uncertainty (and therefore energy) far larger than what's actually observed escaping nuclei, ruling out electrons living inside.
- The uncertainty principle doesn't apply at nuclear scales.
- Confinement to nuclear scale would require an unusually small momentum uncertainty.
2 · Set Up
- Open the gamma-confinement preset and press Reset. This preset models a 100 MeV photon confined near femtometre (10⁻¹⁵ m) scale.
- Enable the minimum-momentum-uncertainty readout.
- Set the confinement region Δx for each trial (near nuclear scale) and record the minimum possible momentum uncertainty.
3 · Collect Data
| Confinement region Δx (nm) | Momentum uncertainty Δp (×10⁻²⁰ kg·m/s) (×10⁻²⁰ kg·m/s) |
|---|---|
| 5e-7 | |
| 0.000001 | |
| 0.000002 |
Plot Δp (y-axis) against 1/Δx (x-axis) for your three trials.
4 · Analyze
- For one trial, compute Δp_min = ℏ/(2Δx) using ℏ = 1.055×10⁻³⁴ J·s. Compare to the table — notice these values are about 10⁵ times larger than the heisenberg-electron experiment's, because Δx here is about 10⁵ times smaller.
- For a photon, momentum relates to energy by p = E/c. Explain how converting your Δp_min values to an equivalent minimum energy uncertainty (multiply by c) helps justify why particles confined to nuclear dimensions must carry enormous minimum energy — tens of MeV, matching this experiment's 100 MeV photon.
5 · Extend
- Historically, physicists once wondered if electrons emitted in beta decay were 'stored inside' the nucleus beforehand. This uncertainty-principle argument (electrons confined to nuclear scale would need far more energy than beta-decay electrons actually have) was key evidence that electrons are instead CREATED at the moment of decay, not pre-existing inside the nucleus.
- Unlike the electron in heisenberg-electron, this experiment explicitly models a massless photon, using momentum p = E/c instead of p = √(2mK). Explain why a photon's momentum formula has to be different from a massive particle's.
The Physics Behind This Experiment
Uncertainty at Nuclear Scale
Confining any particle — including a massless photon — to within Δx ≈ 10⁻¹⁵ m demands a minimum momentum uncertainty Δp ≥ ℏ/(2Δx) on the order of 10⁻²⁰ kg·m/s, corresponding to energies far exceeding what's observed for particles actually found inside nuclei.