Homework Help: Nuc Phys - Use the uncertainty principle to estimate the min speed of alpha particle

1. Apr 27, 2009

wdednam

1. The problem statement, all variables and given/known data

Use the uncertainty principle to estimate the minimum speed and kinetic energy of an alpha particle confined to the interior of a heavy nucleus.

2. Relevant equations

delta_p*delta_r = h_bar/2 for minimum momentum

p = mv for non-relativistic particle, the alpha particle in this case

T = p^2/2m where m = rest mass of alpha particle

I'm using Krane's Introductory Nuclear Physics and the book gives for a typical heavy nucleus, r = a = 7.5 fm. Chapter 8 section 8.4.

3. The attempt at a solution

I calculated p using p*a = h_bar/2 for a = 7.5 fm. But when I plugged this into T to get the minimum kinetic energy I got something of the order of 0.1 MeV for the alpha particle confined inside the nucleus.

In the textbook it says that the kinetic energy of an alpha particle inside a typical heavy nucleus is around Q + V0 = 6 MeV + 35 MeV = 41 MeV where V0 is the depth of the potential well to which the alpha particle is confined and Q the disintegration energy.

I don't know what I'm doing wrong here. Any help would be appreciated, thanks.