Thorium-232 emits an alpha particle of about MeV and has a half-life of years

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Nuclear Physics · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Free particles, wave packets and tunnelling

Problem

Thorium-232 emits an alpha particle of about

4.0

MeV and has a half-life of

1.4\times10^{10}

years. Radon-220 emits one of about

6.4

MeV and has a half-life of

55.6

s. Model both with the same stand-in rectangular barrier,

22

MeV high and

25

fm wide, chosen as round numbers and not fitted to either half-life. Using

m_\alpha c^2 = 3727.4

MeV and

\hbar c = 197.3

MeV fm, find the ratio of

e^{-2\kappa a}

at the two alpha energies, compare it with the measured ratio of half-lives, and say what the size of the gap tells you about the real barrier.