{"id":4381,"date":"2024-09-22T17:06:29","date_gmt":"2024-09-22T17:06:29","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=4381"},"modified":"2024-09-22T17:06:30","modified_gmt":"2024-09-22T17:06:30","slug":"rutherfords-alpha-scattering-experiment","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/09\/22\/rutherfords-alpha-scattering-experiment\/","title":{"rendered":"RUTHERFORD\u2019S ALPHA-SCATTERING EXPERIMENT"},"content":{"rendered":"\n

Meanwhile, Rutherford\u2019s colleague Hans Geiger was exploring the use of thin films of mica\u2014a transparent mineral that can be split into very thin slices\u2014as radiation windows for his detector tubes. Geiger noticed that mica spread out a beam of alpha radiation by slightly deflecting some of its alpha particles. Together with Ernest Marsden\u2014a young undergraduate student working for Rutherford\u2014Geiger found that weak reflections could be detected from a beam of alpha particles directed toward some metals. Although the \u201cplum-pudding\u201d model of the atom could explain some of the alpha-particle scattering in mica, one wouldn\u2019t expect to see any alpha particles to bounce back when hitting the gelatinous \u201cpudding.\u201d<\/p>\n\n\n\n

Armed with these clues, Rutherford designed an experiment to measure the scattering and reflections of alpha particles using an extremely thin gold leaf.\u00a0Figure 69a\u00a0shows a simplified diagram of Rutherford\u2019s apparatus. In it, a stream of alpha particles was aimed at an extremely thin (under 0.1 \u03bcm) gold foil. Geiger and Marsden spent months in the darkroom counting scintillations on a fluorescent screen that could be rotated around the foil. They found that almost all of the alpha particles went straight through the gold foil, continuing on a straight-line path until they hit the fluorescent screen. Some of the alpha particles were deflected slightly, usually 2\u00b0 or less. However, just a very few alpha particles\u2014around one in 20,000\u2014bounced off the foil at an angle of 90\u00b0 or more.<\/p>\n\n\n\n

Figure 69\u00a0In Rutherford\u2019s scattering experiment, (a<\/strong>) when a beam of alpha particles is directed at a thin gold foil, most particles pass through the foil undeflected, but some are deflected at an angle, and a few even reflect back toward the particle source. (b<\/strong>) This could not happen unless atoms are made mostly of empty space, and only the alpha particles that graze or strike a small, solid nucleus are deflected.\"\"<\/p>\n\n\n\n

Rutherford found the latter to be completely incompatible with the \u201cplum pudding\u201d model. As he is often quoted: \u201cIt is as if you fired a 15-inch artillery shell at a sheet of tissue paper and it came back to hit you!\u201d<\/p>\n\n\n\n

Rutherford\u2019s solution to the riddle of large- and small-angle scattering was to concentrate the atom\u2019s mass in a very small space we now call the\u00a0nucleus<\/em>. While Thomson\u2019s \u201cplum-pudding\u201d model spread the entire mass of the atom throughout a sphere of radius 10\u221210<\/sup>\u00a0m (Figure 55), Rutherford placed most of the mass at the center of the atom, in a space much smaller than the gold atom itself, which he calculated to be smaller than 34 \u00d7 10\u221215<\/sup>\u00a0m in radius. We now know that the radius of the gold atom is about 7.5 fm (femto = 10\u221215<\/sup>), while the radius of a single proton (the nucleus of a hydrogen atom) is only 0.88 fm.<\/p>\n\n\n\n

As shown in\u00a0Figure 69b, the nucleus is so small that in the highest probability an alpha particle would just fly through the gold foil as if nothing were there. Some alphas passed near some gold atom nuclei, and were slightly deflected. The gold sheet used in the experiment was some 50 atoms thick, so some of the alpha particles were deflected by more than one close encounter with a gold nucleus, causing scattering of up to 2\u00b0. However, a very, very few alpha particles hit a nucleus smack-on. Since the alpha particle is positively charged, it is repelled by the equally charged nucleus with such force that it may bounce back toward its source.<\/p>\n\n\n\n

Replicating Rutherford\u2019s experiment in its original form requires an enormous amount of patience and dedication. Geiger and Marsden\u2019s months in the darkroom counting scintillations through a microscope eyepiece was so traumatic, it is said, that Geiger\u2019s motivation for developing the GM tube was to replace his tired eyes by an automatic detector.<\/p>\n\n\n\n

The following is an experiment that you should definitely try so that you can empathize with Geiger\u2019s aggravation: purchase a small screen coated with silver-activated zinc sulfide and look at it through a magnifying glass or jeweler\u2019s loupe. After adapting your eyes to darkness, you will be able to see the faint scintillations produced on the screen when it is exposed to a source of alpha particles. Each flash of light is the result of a single alpha particle interacting with the activated ZnS. Back in 1903, Sir William Crookes (remember him?) built the first device of this kind and named it spinthariscope<\/em>.<\/p>\n\n\n\n

You can buy the screen for less than $15 from GeoElectronics, and use one of the sources of alpha radiation that we have discussed. For example, you could use a 210<\/sup>Po disk source, a lantern mantle containing 232<\/sup>Th, or the small button containing 241<\/sup>Am from a smoke detector (but only if you are in a country that allows you to take one apart legally). You could also purchase a ready-made spinthariscope, complete with a tiny radioactive speck, from United Nuclear.<\/p>\n\n\n\n

If catching the flashes produced by a source just under the zinc sulfide screen requires effort, just imagine what it takes to catch one in 20,000 particles in the direction of the backscattered radiation! We are sure that you now have a whole new appreciation for the devotion Geiger and Marsden had for their work.<\/p>\n\n\n\n

There are a few modern ways of conducting Rutherford\u2019s scattering experiment in a more convenient way. One popular device used in many colleges is based on a design by Charles W. Leming of Henderson State University in Arkansas. It uses a special plastic-sensitive film to record particle hits. The film is exposed inside a vacuum chamber for at least 7 days, after which it is \u201cdeveloped\u201d in a sodium hydroxide (caustic soda) solution. A stereo microscope is then used to look at the film and count alpha particles deflected by up to \u00b120\u00b0.<\/p>\n\n\n\n

The film is made by Kodak-Path\u00e9 in France (type LR115-II),22<\/sup> and consists of a 13-\u03bcm-thick red layer of cellulose nitrate over 100-\u03bcm-thick clear polyester film. Alpha particles damage the nitrocellulose, and the film can be etched to reveal the impact spots by soaking it for 24 hours in a 2.5 molar solution of NaOH|| ||<\/sup><\/a> at a temperature of 40\u00b0C. The individual pits can be viewed under a microscope at 50\u2013200x magnification. The film is rather expensive, but can be purchased from the Science Source (catalog number EN-21) as replacement film for their commercial version of Leming\u2019s apparatus for studying alpha scattering.<\/p>\n\n\n\n

The now-extinct \u201cAmateur Scientist\u201d column in the February 1986 issue of\u00a0Scientific American<\/em>\u00a0described the amateur device built by Rudy Timmerman of Wickes, Arkansas, to measure alpha-particle scattering using this method.59<\/sup>\u00a0Figure 70a\u00a0shows the basic configuration used in Timmerman\u2019s design, as well as in the commercial Rutherford Scattering Apparatus made by Daedalon (Science Source model EN-20). Typical results are shown in\u00a0Figure 70b. Counts are normalized to those at 2.5\u00b0, since the number of hits within this scattering angle is simply enormous. The curve agrees with the data originally obtained by Geiger and Marsden, as well as with the formula that Rutherford worked out for the scattering of alpha particles by gold nuclei.20<\/sup><\/p>\n\n\n\n

Figure 70\u00a0A popular educational apparatus to measure alpha scattering by a thin gold foil uses this simple setup.\u00a0(a)<\/strong>\u00a0Alpha particles from a\u00a0210<\/sup>Po source at the top of the chamber are collimated into a fine beam by an aluminum disk with a small hole. The beam hits a thin foil of gold leaf. An alpha particle\u2013sensitive film records impacts by direct and scattered particles. The stack is placed inside a plastic bell jar, which is kept at a moderate vacuum for 7 days. The figure is not to scale in order to show detail.\u00a0(b)<\/strong>\u00a0A graph of particle strikes that can be counted under a microscope. These strikes appear on the film as clear spots in a red background after development in a caustic soda bath.\"\"<\/p>\n\n\n\n

Our homemade version of the apparatus is shown in Figure 71<\/a>. We use two radioactive sources to produce two fine alpha-particle beams. However, only one of the two alpha-particle beams undergoes Rutherford scattering, allowing direct comparison between alpha-particle dispersion due to beam divergence and due to Rutherford scattering.<\/p>\n\n\n\n

Figure 71\u00a0Our version of the alpha-scattering apparatus uses an unmodified Staticmaster\u00ae<\/sup>\u00a0cartridge to produce two fine alpha-particle beams.\u00a0(a)<\/strong>\u00a0Only one of the two alpha-particle beams undergoes Rutherford scattering, allowing direct comparison between alpha-particle dispersion due to beam divergence and due to Rutherford scattering.\u00a0(b)<\/strong>\u00a0The apparatus must be operated inside a vacuum chamber during exposure, as alpha particles have very limited range in air, but the vacuum requirements are not stringent. A student-grade polycarbonate vacuum chamber is sufficient.\"\"<\/p>\n\n\n\n

The availability of alpha-particle sources that can be purchased without special licensing requirements is very limited. One popular source used by experimenters is a 1 \u03bcCi 241<\/sup>Am button extracted from an ionization-type smoke detector. However, this practice is illegal in the United States. For this reason, the Daedalon Rutherford scattering apparatus uses an exempt 210<\/sup>Po source with a maximum activity of 0.1 \u03bcCi. As an alternative, we use a static eliminator cartridge (StaticMaster) that contains two metallic foils plated with 210<\/sup>Po. We make legal use of the sources within the cartridge (with a total activity of 500 \u03bcCi), since we do not modify the cartridge in any way. It must be noted that the predominant 5.30 MeV emission from 210<\/sup>Po has a half-life of 138.3 days, so the cartridge would need semi-annual replacement if the setup is used as part of a regular didactic lab course.<\/p>\n\n\n\n

We purchased 23-karat gold leaf at a gourmet cooking store, where it is sold as thin leaves for use as decorations on foods. The ones we used were made by Fabbriche Riunite Metalli in Foglie e in Polvere S.p.A. (Morimondo, Italy). It must be noted that handling the gold leaf and attaching it to the holder plate requires extreme care. The gold leaf is so thin that it shreds at the lightest touch. It is best handled with a brush that is charged with some static electricity by rubbing it lightly on the skin. We placed a few tiny drops of model-airplane glue on the frame, and allowed these to grab hold of the gold leaf. We use two layers of this leaf to make it thick enough to yield easily observable alpha-particle scattering.<\/p>\n\n\n\n

We fabricated the frame for the apparatus out of 1<\/sup>\/8<\/sub>-in.-thick aluminum sheet. We drilled the collimation holes with a 1<\/sup>\/16<\/sub>-in. bit. We also drilled coaxial holes on the film support plate through which we could shine a laser pointer to aid in aligning the aluminum plates. A thin aluminum sheet shields the part of the alpha particle-sensitive film recording the unscattered beam from alpha particles that may be scattered by the gold foil at wide angles.<\/p>\n\n\n\n

The apparatus must be operated inside a vacuum chamber during exposure, because alpha particles have very limited range in air. The vacuum requirements for this setup are not stringent at all. The range of the 210<\/sup>Po 5.30-MeV alpha particles at atmospheric pressure is approximately 3.8 cm. Since the kinetic energy loss experienced by alpha particles scales linearly with pressure, evacuating the chamber to approximately 1\/1000 of normal atmospheric pressure ensures that alpha particles can travel virtually unimpeded by air between the source and the LR115-II film. In addition, since this film is not sensitive to light or other types of radiation besides alpha particles and neutrons (such as beta or gamma rays), the chamber can be transparent without affecting the results of the experiment. As such, a student-grade poly-carbonate vacuum chamber (e.g., 4.7-L Thermo Scientific Nalgene\u00ae<\/sup> vacuum chamber) suffices for this experiment.<\/p>\n\n\n\n

We connected the vacuum chamber through a short length of vacuum-service rubber tubing to a hose-to-KF16 vacuum flange adapter. We terminated the KF16 port with a vacuum valve so we could periodically lower the pressure in the vacuum chamber using our refrigeration-service vacuum pump (Robinair model 15600). We also took pressure readings twice every day to make sure that the chamber was holding its vacuum below 1 Torr.<\/p>\n\n\n\n

A portion of our etched LR115-II film is shown in Figure 72<\/a>. The spot on the left-hand side of the picture was produced by the collimated beam, while the one on the right was produced when the alpha particles underwent Rutherford scattering. The number of scattered particles drops rapidly with increasing scattering angle, so we show only scattering out to 6\u00b0. However, the setup is able to register scattered particles out to 20\u00b0.<\/p>\n\n\n\n

Figure 72\u00a0Alpha-particle hits on the Kodak-Path\u00e9 LR115-II film are shown after it is etched for 24 hours in 2.5 N NaOH at 40\u00b0C.\u00a0(a)<\/strong>\u00a0The collimated beam.\u00a0(b)<\/strong>\u00a0Alpha-particle beam that has been scattered by a thin gold film.\"\"<\/p>\n\n\n\n

A lower-cost alternative to LR115-II film is plastic chips that are commonly used in neutron dosimeters and home radon test kits. The chips are of a plastic known as CR-39, which is commonly used in the manufacture of eyeglass lenses. When exposed to neutrons or alpha particles, the plastic is microscopically damaged at the impact sites. Just as with the LR115, the pits can then be enlarged sufficiently to be viewed with a 200 \u00d7 microscope by etching the chips in a caustic solution of sodium hydroxide (6 N NaOH at 70\u00b0C for 7 hours). We purchased the CR-39 dosimeter chips from Landauer for $3 apiece. Each chip measures 19 mm \u00d7 9.4 mm \u00d7 0.9 mm and is individually etched with a serial number for identification. As shown in\u00a0Figure 73, one of the chips records alpha particles that spread only due to beam divergence after collimation. The other chip records alpha particles scattered by the gold foil within the range of \u03b8 = \u00b117\u00b0.\u00a0Figure 74\u00a0shows our results after a 7-day exposure.<\/p>\n\n\n\n

Figure 73\u00a0Inexpensive CR-39 plastic dosimetry chips can be used instead of the Kodak-Path\u00e9 LR115-II film to record the collimated and Rutherford-scattered alpha particles.\u00a0(a)<\/strong>\u00a0The dimensions given here allow alpha particles to be recorded out to a scattering angle of \u03b8 = \u00b1 17\u00b0.\u00a0(b)<\/strong>\u00a0The setup is sufficiently small to fit within a small student-grade polycarbonate vacuum chamber.\u00a0(c)<\/strong>\u00a0Two layers of 23-karat gold leaf are tacked with tiny drops of model-airplane glue.\"\"<\/p>\n\n\n\n

Figure 74\u00a0Alpha-particle hits on CR-39 plastic chips after etching for 7 hours in 6 N NaOH at 70\u00b0C.\u00a0(a)<\/strong>\u00a0The collimated beam.\u00a0(b)<\/strong>\u00a0Alpha-particle beam that has been scattered by a thin gold film.\"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

Meanwhile, Rutherford\u2019s colleague Hans Geiger was exploring the use of thin films of mica\u2014a transparent mineral that can be split into very thin slices\u2014as radiation windows for his detector tubes. Geiger noticed that mica spread out a beam of alpha radiation by slightly deflecting some of its alpha particles. Together with Ernest Marsden\u2014a young undergraduate […]<\/p>\n","protected":false},"author":1,"featured_media":4174,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[513],"tags":[],"class_list":["post-4381","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-atoms-and-radioactivity"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/09\/atom-2.png","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=4381"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4381\/revisions"}],"predecessor-version":[{"id":4382,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/4381\/revisions\/4382"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/4174"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=4381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=4381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=4381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}