Details of Calculating Maximal Nuclear Size
For head on collisions between alpha particles and the nucleus, all the kinetic energy of the alpha particle is turned into potential energy and the particle is at rest. The distance from the centre of the alpha particle to the centre of the nucleus (b) at this point is a maximum value for the radius, if it is evident from the experiment that the particles have not hit the nucleus.
Applying the inverse-square law between the charges on the electron and nucleus, one can write:
Rearranging:
For an alpha particle:
- m (mass) = 6.7×10−27 kg
- q1 = 2×(1.6×10−19) C
- q2 (for gold) = 79×(1.6×10−19) C
- v (initial velocity) = 2×107 m/s
Substituting these in gives the value of about 2.7×10−14 m. (The true radius is about 7.3×10−15 m.) The true radius of the nucleus is not recovered in these experiments because the alphas do not have enough energy to penetrate to more than 27 fm of the nuclear center, as noted, when the actual radius of gold is 7.3 fm. Rutherford realized this, and also realized that actual impact of the alphas on gold causing any force-deviation from that of the 1/r coulomb potential would change the form of his scattering curve at high scattering angles (the smallest impact parameters) from a hyperbola to something else. This was not seen, indicating that the gold had not been "hit" so that Rutherford only knew the gold nucleus (or the sum of the gold and alpha radii) was smaller than 27 fm (2.7×10−14 m)
Read more about this topic: Rutherford Scattering
Famous quotes containing the words details of, details, calculating, nuclear and/or size:
“Patience is a most necessary qualification for business; many a man would rather you heard his story than granted his request. One must seem to hear the unreasonable demands of the petulant, unmoved, and the tedious details of the dull, untired. That is the least price that a man must pay for a high station.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“There was a time when the average reader read a novel simply for the moral he could get out of it, and however naïve that may have been, it was a good deal less naïve than some of the limited objectives he has now. Today novels are considered to be entirely concerned with the social or economic or psychological forces that they will by necessity exhibit, or with those details of daily life that are for the good novelist only means to some deeper end.”
—Flannery O’Connor (1925–1964)
“I know that the right kind of leader for the Labour Party is a kind of desiccated calculating machine.”
—Aneurin Bevan (1897–1960)
“Language is as real, as tangible, in our lives as streets, pipelines, telephone switchboards, microwaves, radioactivity, cloning laboratories, nuclear power stations.”
—Adrienne Rich (b. 1929)
“There are obvious places in which government can narrow the chasm between haves and have-nots. One is the public schools, which have been seen as the great leveler, the authentic melting pot. That, today, is nonsense. In his scathing study of the nation’s public school system entitled “Savage Inequalities,” Jonathan Kozol made manifest the truth: that we have a system that discriminates against the poor in everything from class size to curriculum.”
—Anna Quindlen (b. 1952)