San José State University |
---|
applet-magic.com Thayer Watkins Silicon Valley & Tornado Alley USA |
---|
Integral Alpha Particle Nuclides |
The binding energy of the He4 nucleus, the alpha particle, is relatively high compared to that of close by nuclides. It is 28.3 million electron volts (MeV) compared with 2.2 MeV for the H2, deuteron, 7.7 MeV for the He3 and 8.5 MeV for the H3, tritium, nuclides. On the other hand for nuclides which include the components of the alpha particle plus additional nucleons the binding energies at the 28 MeV level. This suggest that when the components of an alpha particle are present, two protons and two neutrons, such a particle is formed.
When the binding energies of nuclides which could contain an integral number of alpha particles are reviewed, as in the table below, one finds that there is generally an excess in binding energy above that which could be attributed to the formation of alpha particles.
The Binding Energies of Nuclei Which Could Contain an Integral Number of Alpha Particles |
||||||
---|---|---|---|---|---|---|
Element | Neutrons | Protons | Binding Energy |
Number of Alpha Particles |
Binding Energy |
Difference |
He | 2 | 2 | 28.295674 | 1 | 28.295674 | 0 |
Be | 4 | 4 | 56.49951 | 2 | 56.591348 | 0.091838 |
C | 6 | 6 | 92.161728 | 3 | 84.887022 | 7.274706 |
O | 8 | 8 | 127.619336 | 4 | 113.182696 | 14.43664 |
Ne | 10 | 10 | 160.644859 | 5 | 141.47837 | 19.166489 |
Mg | 12 | 12 | 198.25689 | 6 | 169.774044 | 28.482846 |
Si | 14 | 14 | 236.53689 | 7 | 198.069718 | 38.467172 |
S | 16 | 16 | 271.78066 | 8 | 226.365392 | 45.415268 |
Ar | 18 | 18 | 306.7157 | 9 | 254.661066 | 52.054634 |
Ca | 20 | 20 | 342.052 | 10 | 282.95674 | 59.09526 |
Ti | 22 | 22 | 375.4747 | 11 | 311.2524 | 64.22229 |
Cr | 24 | 24 | 411.462 | 12 | 339.548088 | 71.913912 |
Fe | 26 | 26 | 447.697 | 13 | 367.843762 | 79.853238 |
Ni | 28 | 28 | 483.988 | 14 | 396.139436 | 87.848564 |
Zn | 30 | 30 | 514.992 | 15 | 424.43511 | 90.55689 |
Ge | 32 | 32 | 545.95 | 16 | 452.730784 | 93.219216 |
Se | 34 | 34 | 576.4 | 17 | 481.026458 | 95.373542 |
Kr | 36 | 36 | 607.1 | 18 | 509.322132 | 97.777868 |
Sr | 38 | 38 | 638.1 | 19 | 537.617806 | 100.482194 |
Zr | 40 | 40 | 669.8 | 20 | 565.91348 | 103.88652 |
Mo | 42 | 42 | 700.9 | 21 | 594.209154 | 106.690846 |
Ru | 44 | 44 | 731.4 | 22 | 622.504828 | 108.895172 |
Pd | 46 | 46 | 762.1 | 23 | 650.800502 | 111.299498 |
Cd | 48 | 48 | 793.4 | 24 | 679.096176 | 114.303824 |
Sn | 50 | 50 | 824.9 | 25 | 707.39185 | 117.50815 |
The graph of the excess binding energy shown as the last column in the above table displays some interesting characteristics.
There is no significant excess binding energy for two alpha particles but for three there is. The additional binding energy for the number of alpha particles above two is roughly constant at about 7 MeV per additional alpha particle until a level of 14 alpha particles is reached. Thereafter the increase is about 3 MeV per additional alpha particle, as shown below.
This suggests that the equation which would fit the data for the binding energies of the integral alpha particle nuclides is of the form
where #α is the number of alpha particles and u(z) is the ramp function such that if z<0 then u(z)=0 and otherwise u(z)=z. The coefficients c_{1} and c_{2} are positive and c_{3} negative.
A multiple regression of the binding energies of the integral alpha particle binding energies on functions of the number of alpha particles yields
BE = 29.25983#α + 5.83034u(#α-2) −4.76477u(#α-14) [22.3] [4.2] [-15.3] R² = 0.999917
The figures in square brackets below the coefficients are the t-ratios for the coefficients, the ratio of the coefficient to its standard deviation. The statistical fit is quite good.
The value of 29.25983 MeV for the effect of an alpha particle on binding energy instead of 28.29567 MeV, the binding energy of a single alpha particle, could be construed to be evidence that the 28.29567 MeV is an underestimate. Such an underestimate could come as result of the mass of a neutron being underestimated by 0.48 MeV, about one electron rest mass energy.
(To be continued.)
HOME PAGE OF Thayer Watkins |