dlid by
J. DUDLEY HERRON Purdue University Wesl Latayene, Indiana 47907
Rutherford and the Nuclear Atom J. Dudley Herron Purdue University West Lafayette, Indiana Perhaps it is enough that we get students to draw the correct conclusions,and we should not worry that they misunderstand the reasoning leading to them. Still, it would be nice to have them get the rieht answer for the right reason. The Rutherford experTment (actually a series of experiments done by Geiger and Marsden in Rutherford's laboratory) is a case in point. Most chemistry studenh know the facts of the experiment; that most of the alpha particles in the heam aimed a t a thin layer of gold foil (about 0.00004 cm thick) passed through the foil undeflected but that a small fraction of the particles were bent through rather large angles. These students also know that. as a result of Rutherford's analysis of these results, Thomson's idea that an atom consisted of negatively charged "cor~uscles"embedded in a sphere of uniformly distributed positive electricity was abandoned in favor of the nuclear atom. Where students err is in their understanding of the basis for that -.~ - - conclusion. ~-~~~~~~~ - ~ ~ Students get the impression that the surprising part of this ex~eriment was that most aloha c articles ~ a s s e dthrough the -~~ gold foil undeflected, the onl; po&ible explanation being that atoms are mostly empty space with the mass of the atom concentrated in a small region of space a t the center. But it a Pass through the foil is not the fact that the a l ~ h particles that leads to the conclusi~nof nuclearatom but i t h e r , that some are deflected. The following quotation from Rutherford's paper'on "The Scattering o f ~ i ~ and h a Beta Particles bv Matter and the Structure of the Atom"' makes this point clear. ~~~~~~~
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It is well known that the alpha and heta particles suffer deflexions from their rectilinear paths by encounters with atoms of matter. This scattering is far more marked for the heta than for the alpha particle on account of the much smaller momentum and energy of the former particle. There seems to he no doubt that such swiftly moving particles pass through the atoms in their path, and that the deflexionsohserved are due to the strong electric field traversed within the atomic system. It has generally been supposed that the scatteringof a pencil of alpha or heta rays in passing through a thin plate of matter is the result of a multitude of small scatteringsby the atoms of matter traversed.The observations, however, of Geiger and Marsden on the scattering of alpha rays indicate that some of the alpha particles must suffer a deflexion of more than aright angle at a single encounter. They found, for examole. . .that a small fractionof the incidentalpha particles, about 1in 20,000, were turned through an average angie of90' in passing thmrrch n laver of eold-foilabout 0.00004 cm thick.. .Asim~le cal......- .-.-,culation hased on the theory of probability shows that the chance of an alpha particle being deflected through 90" is vanishingly small ~~~
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Recently Sir J.J. Thomson has put forward a theory to explain the scattering of electrified particles in passing through small thicknesses of matter. The atom is suowsed to consist of a number Nof negatively .. charged corpuscles, ncrompanied h y an equal quantity of &sitwe rlerrr~rityunifurrnly distributed throughout a sphere.. . T h e detlexion of the particle in passing through thearom is ~upporcdt o he small.. . In comparing the theory outlined in this paper with the experi~
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mental rsults, it hes been s u p d that theatom conaktsof srentral charge supposed cnncenrrated at a point, and that the large single dpflexioni of the alpha and he- particles are mainly due to their passage through the strong central field. If the Thomson model of the atom were correct, i t would be no surprise whatsoever to find that particles with the mass and momentum of the alpha particles used in Geiger and Marsden's experiments passed through a thin foil unaffected. The uniform distribution of charge in the atom would have virtually no effect. Thus, it was the 1in 20,000 particles deflected +rough large angles that led Rutherford to postulate that the positive charge in the atom is concentrated in a small reeion of mace a t its center and the idea of a nuclear atom became est'ablished as the accepted theory. 'Rutherford, E., Phil.Mag. ser. 6, xai, 669 (May, 1911).Reprinted in "The Collected Papers of Lord Rutherford,Volume 2" New York, Interscience Publishers, Inc., 1963, pp. 238-54.
Frequency Distribution Curves for 1s Electrons V. L. Chapman University of British Columbia Vancouver, Canada The fundamental idea underlying the quantum mechanical atom is the probability of finding an electron (say, a 1s electron) a t a particular distance from the nucleus. While orbitals renresentvolumes in mace with definite conformations, the idka of where the election is most likely to be found a t adistance R. is both useful and desirable. We talk about darthoards &d beehives, comparing the dart boles in the hoard or the bees to electron Dosition orohabilities. Two ideas can be inv&igated;-(1) the density of the electron fields, and (2) the probability of finding an electron at some position, by analogy. The following investigation has been tried successfully with three Chemistry 12 classes. Obtain a piece of hardboard or m i o n i t e 8% X 11 in. or larger. On a ditto master draw a target having six concentric circles with radii on 1cm, 3 cm, 5 cm, 7 cm, gem, and 11cm. Place the master on the hardboard and cover it with a piece of flexible plastic such as an overhead transparency sheet. Attach these to the board wih masking tape. Prepare a dart of the type used in dart hoard competition. Get the metal shop to weld or braze a blob on the point of the dart. If necessarv. file i t off and round the end so i t will not puncture the pla%c when used. Droo the dart on the tareet aimine a t the hullseve, from a t least three feet above. For more uncertain results use two hands and hold the feathers between the thumb and forefinger of both hands. After about 200 trials, lift the plastic, remove the target and reproduce a copy for each member of the class. Count the dots in the bullseye and in each annulus (ring). Dividing the target into sectors reduces the uncertainty in counting. Determine the area of each ring and also the area of the Volume 54, Number 8, August 1977 1
499
bullseye. The area of each annulus is u(R
R and r are the outer and inner radii.
+ r)(R - r ) where
Determine the average radius of each annulus. A linear arithmetic average is satisfactory although it is possible to calculate the radius that divides the annulus into two equal areas. Assumine that 200 trials are sienificant. calculate the pn,babiliti"f finding a dot in each ;;f.the sin areas. This can bedone by finding theBof the total trials that fall withineach area. Plot a eraoh .. . to show the deoendence of the densitv of dots on the average distance from the center for each area. Also. d o t a maoh to show the orobabilitv of a dot comoared to its d&tancLfrom the center ;sing the average radii of the annuli for this value. If a teacher wishes, he could use the target provided here to prepare an overhead transparency by using a photocopier. He might also use the two graphs provided for the same purpose. The data in the table were determined from the target illustrated, and the calculations made. radius Ring inner outer # (cml
Average R
(arithl (cml
Aver-
ageR (equal areal
No. of Dots
Annuli (cm'l
Ales of Denrify
% Probability
lenmeyer flasks containing samples of the different oxidation states of vanadium: blue vanadium(IV), green vanadium(III), and violet vanadium(I1). These s a m ~ l e scan be prepared in advance and aid in the ire-lab discussion as well as serving as a color guide for the students while they are performing the titration. The samples of the different oxidation states of vanadium will remain stable if stored in tightly stoppered flasks. Vanadium(I1) will remain stable if a 25-ml Erlenmeyer flask is almost completely filled and then tightly stoppered with a rubber stopper. The problem of aerial oxidation of vanadium(I1) should be discussed during the demonstration and pre-lab discussion. The students perform the oxidation of the vanadium by titrating it with 0.1 M potassium permanganate. Each student is given 10 ml of vanadium(I1) and the titration is begun promptly. As the students perform the titration, they can compare the color of their sample to those prepared earlier by the teacher. As an end product of the oxidation, the students obtain a yellow sample of vanadium(V). This experiment supplements the high school laboratory program, and a great deal of information can be related to the experiment. Writing a laboratory report on the experiment serves as a review of oxidation-reduction equations. The changes taking place may be summarized in the following equations V(I1) + V(II1) V(IV) V(V) Violet Green Blue Yellow 5V2++ MnOl- + 8Hf Mn2+ + 4Hz0 + 5V3+ 5V3++ MnOi- + 8H+ MnZC+ 4Hz0 + 5V4+ 5V4++ +no4- + 8Ht Mn2+ + 4Hz0 + 5VSt +
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Vanadium for High School Students A. Ward Grant, Jr. Brockton High School Brockton, Massachusetts 02402 The titrimetric determination of the oxidation states of vanadium has been discussed as a suitable exoeriment for college students,' and with minor adaptations, the experiment is audirnhle for hieh school students. The tpacher can ~erform .. the reduction of an aqueous solution of vanadium&') as a demonstration, and the students can perform the oxidation of the vanadium(I1) back to its original state. Prior to the lab period, prepare the solution by dissolving 2 g of ammonium metavanadate in 50 ml of 1M sodium hydroxide solution. While stirring the resulting solution, add 80 ml of 3 M sulfuric acid, and then dilute to 250 ml with distilled water. This solution of vanadium(V) is now ready for the demonstration. Fill a separatory funnel approximately one-third full of 30 mesh zinc. Pour the solution of vanadium(V) into the separatory funnel and allow it to flow over the zinc. As the vanadium passes over the zinc i t is reduced to the vanadium(I1) oxidation state and the solution is collected in a flask. The students are reedily aware of the reaction, and the progress is vividly demonstrated as the color changes from yellow, to blue, t o green, and eventually to violet. The teacher may have Er-
500 1 JouMl of Chemical Education
Students often have difficulty visualizing the concept of different oxidation states. The different colors, resulting from the different oxidation states of vanadium, make this principle easier to comprehend. The teacher can also extend the postlab discussion to show that the different colors result in part from the loss of 3d electrons, thus relating the concept of oxidation and reduction to atomic structure. The CHEM film "Vanadium: A Transition Element" is an excellent summation of the post-lab discussion. Davis, J. M., J. CHEM. EDUC., 45,473 (1968).
Errata In the July 1976 High School Forum, the equation Hgzt
should read Hg?+
-
2 Hg2+
+ 2e
2 HgZ+
+ 2e-
In the final section of the June 1976 High School Forum it is suggested that NO, NO2 and or Hz may be products of a reaction between Mg and 6 M HNOs. Charles Rutenber, Elmira College, Elmira, New York points out that Mg is a strong reducing agent and that the reported results can be explained by HNOs being reduced to NH3. Neutralization of the solution with 6 M NaOH will result in the characteristic odor of NH3.
