{"id":25326,"date":"2019-10-22T15:49:07","date_gmt":"2019-10-22T15:49:07","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=25326"},"modified":"2023-06-14T10:50:29","modified_gmt":"2023-06-14T10:50:29","slug":"gray-unit-of-radiation-dose","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/radiation-protection\/absorbed-dose\/gray-unit-of-radiation-dose\/","title":{"rendered":"Gray &#8211; Unit of Radiation Dose"},"content":{"rendered":"<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<p><strong>Absorbed dose<\/strong> is defined as the amount of energy deposited by ionizing radiation in a substance. The <strong>absorbed dose<\/strong> is given the symbol <strong>D<\/strong>. The absorbed dose is usually measured in a unit called the <strong>gray<\/strong> (Gy), derived from the SI system. The non-SI unit <strong>rad<\/strong> is sometimes also used, predominantly in the USA.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-25307\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-definition.png\" alt=\"absorbed dose - definition\" width=\"180\" height=\"72\" \/><\/a><\/p>\n<p>Units of absorbed dose:<\/p>\n<ul>\n<li><strong>Gray<\/strong>. A dose of one gray is equivalent to a unit of energy (joule) deposited in a kilogram of a substance.<\/li>\n<li><strong>RAD<\/strong>. A dose of one rad is equivalent to depositing one hundred ergs of energy in one gram of any material.<\/li>\n<\/ul>\n<h2>Gray &#8211; Unit of Absorbed Dose<\/h2>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/gray_unit_radiation-min.png\"><img loading=\"lazy\" class=\"alignright size-medium wp-image-25313\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/gray_unit_radiation-min-300x267.png\" alt=\"gray unit\" width=\"300\" height=\"267\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/gray_unit_radiation-min-300x267.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/gray_unit_radiation-min-768x683.png 768w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/gray_unit_radiation-min.png 900w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>A dose of <strong>one gray<\/strong> is equivalent to a unit of energy (joule) deposited in a kilogram of a substance. This unit was named in honor of <strong>Louis Harold Gray<\/strong>, who was one of the great pioneers in radiation biology. One gray is a large amount of absorbed dose. A person who has absorbed a whole-body dose of 1 Gy has absorbed one joule of energy in each kg of body tissue.<\/p>\n<p><strong>Absorbed doses<\/strong> measured in the industry (except nuclear medicine) often have usually lower doses than one gray, and the following multiples are often used:<\/p>\n<p><strong>1 mGy (milligray) = 1E-3 Gy<\/strong><\/p>\n<p><strong>1 \u00b5Gy (microgray) = 1E-6 Gy<\/strong><\/p>\n<p>Conversions from the SI units to other units are as follows:<\/p>\n<ul>\n<li>1 Gy = 100 rad<\/li>\n<li>1 mGy = 100 mrad<\/li>\n<\/ul>\n<p>The gray and rad are physical units describing the incident radiation\u2019s physical effect (i.e., the amount of energy deposited per kg). Still, it tells us nothing about the biological consequences of such energy deposition in living tissue.<\/p>\n<h2>Examples of Absorbed Doses in grays<\/h2>\n<p>We must note that<a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radiation\/\"> radiation<\/a> is all around us. In, around, and above the world we live in. It is a natural energy force that surrounds us, and it is a part of our natural world that has been here since the birth of our planet. In the following points, we try to express enormous ranges of radiation exposure, which can be obtained from various sources.<\/p>\n<ul>\n<li><strong>0.05 \u00b5Gy<\/strong> &#8211; Sleeping next to someone<\/li>\n<li><strong>0.09 \u00b5Gy<\/strong> &#8211; Living within 30 miles of a nuclear power plant for a year<\/li>\n<li><strong>0.1 \u00b5Gy<\/strong> &#8211; Eating one banana<\/li>\n<li><strong>0.3 \u00b5Gy<\/strong> &#8211; Living within 50 miles of a coal power plant for a year<\/li>\n<li><strong>10 \u00b5Gy<\/strong> &#8211; Average daily dose received from natural background<\/li>\n<li><strong>20 \u00b5Gy<\/strong> &#8211; Chest X-ray<\/li>\n<li><strong>40 \u00b5Gy<\/strong> &#8211; A 5-hour airplane flight<\/li>\n<li><strong>600 \u00b5Gy<\/strong> &#8211; mammogram<\/li>\n<li><strong>1 000 \u00b5Gy<\/strong> &#8211; Dose limit for individual members of the public, total effective dose per annum<\/li>\n<li><strong>3 650 \u00b5Gy<\/strong> &#8211; Average yearly dose received from natural background<\/li>\n<li><strong>5 800 \u00b5Gy<\/strong> &#8211; Chest CT scan<\/li>\n<li><strong>10 000 \u00b5Gy<\/strong> &#8211; Average yearly dose received from a natural background in Ramsar, Iran<\/li>\n<li><strong>20 000 \u00b5Gy<\/strong> &#8211; single full-body CT scan<\/li>\n<li><strong>175 000 \u00b5Gy<\/strong> &#8211; Annual dose from natural radiation on a monazite beach near Guarapari, Brazil.<\/li>\n<li><strong>5 000 000 \u00b5Gy<\/strong> &#8211; Dose that kills a human with a 50% risk within 30 days (LD50\/30) if the dose is received over a <strong>very short duration<\/strong>.<\/li>\n<\/ul>\n<p>As can be seen, low-level doses are common in everyday life. The previous examples can help illustrate relative magnitudes. From biological consequences, it is very important to distinguish between doses received over <strong>short<\/strong> and <strong>extended periods<\/strong>. An \u201c<strong>acute dose<\/strong>\u201d occurs over a short and finite period, while a \u201c<strong>chronic dose<\/strong>\u201d is a dose that continues for an extended period so that a dose rate better describes it. High doses tend to kill cells, while low doses tend to damage or change them. Low doses spread out over long periods don\u2019t cause an immediate problem to any body organ. The effects of low radiation doses occur at the cell level, and the results may not be observed for many years.<\/p>\n<h2>Calculation of Shielded Dose Rate in grays<\/h2>\n<p>Assume the <strong>point isotropic source<\/strong>\u00a0contains <strong>1.0 Ci of <sup>137<\/sup>Cs<\/strong>\u00a0and has a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-law\/half-life\/\">half-life<\/a> of <strong>30.2 years<\/strong>. Note that the relationship between half-life and the amount of a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/atom-properties-of-atoms\/radionuclide-radioisotope\/\">radionuclide<\/a> required to give an activity of <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/radiation-protection\/units-of-radioactivity\/curie-unit-of-radioactivity\/\">one curie<\/a> is shown below. This amount of material can be calculated using \u03bb, which is the <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/radioactive-decay-law\/decay-constant\/\">decay constant<\/a> of certain nuclide:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/07\/Curie-Unit-of-Activity.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-24886\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/07\/Curie-Unit-of-Activity.png\" alt=\"Curie - Unit of Activity\" width=\"378\" height=\"61\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/07\/Curie-Unit-of-Activity.png 378w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/07\/Curie-Unit-of-Activity-300x48.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/a><\/p>\n<p>About 94.6 percent decays by <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radioactive-decay\/beta-decay-beta-radioactivity\/\">beta emission<\/a> to a metastable <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/atom-properties-of-atoms\/nuclides\/isomers\/\">nuclear isomer<\/a> of barium: barium-137m. The main photon peak of Ba-137m is <strong>662 keV<\/strong>. For this calculation, assume that all decays go through this channel.<\/p>\n<p><strong>Calculate the primary photon dose rate<\/strong>, in gray per hour (Gy.h<sup>-1<\/sup>), at the outer surface of a 5 cm thick lead shield. The primary photon dose rate neglects all secondary particles. Assume that the effective distance of the source from the dose point is <strong>10 cm<\/strong>. We shall also assume that the dose point is soft tissue and it can reasonably be simulated by water, and we use the mass-energy absorption coefficient for water.<\/p>\n<p>See also: <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/interaction-radiation-matter\/interaction-gamma-radiation-matter\/gamma-ray-attenuation\/\">Gamma Ray Attenuation<\/a><\/p>\n<p>See also: <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/atomic-nuclear-physics\/radiation\/shielding-of-ionizing-radiation\/shielding-gamma-radiation\/\">Shielding of Gamma Rays<\/a><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>The primary photon dose rate is <a href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/interaction-radiation-matter\/interaction-gamma-radiation-matter\/gamma-ray-attenuation\/\">attenuated exponentially<\/a>, and the dose rate from primary photons, taking account of the shield, is given by:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/dose-rate-calculation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-25304\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/dose-rate-calculation.png\" alt=\"dose rate calculation\" width=\"671\" height=\"307\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/dose-rate-calculation.png 671w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/dose-rate-calculation-300x137.png 300w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><\/a><\/p>\n<p>As can be seen, we do not account for the buildup of secondary radiation. If secondary particles are produced, or the primary radiation changes its energy or direction, the effective attenuation will be much less. This assumption generally underestimates the true dose rate, especially for thick shields and when the dose point is close to the shield surface, but this assumption simplifies all calculations. For this case, the true dose rate (with the buildup of secondary radiation) will be more than two times higher.<\/p>\n<p>To calculate the <strong>absorbed dose rate<\/strong>, we have to use the formula:<\/p>\n<ul>\n<li>k = 5.76 x 10<sup>-7<\/sup><\/li>\n<li>S = 3.7 x 10<sup>10<\/sup> s<sup>-1<\/sup><\/li>\n<li>E = 0.662 MeV<\/li>\n<li>\u03bc<sub>t<\/sub>\/\u03c1 = 0.0326 cm<sup>2<\/sup>\/g (values are available at NIST)<\/li>\n<li>\u03bc = 1.289 cm<sup>-1<\/sup> (values are available at NIST)<\/li>\n<li>D = 5 cm<\/li>\n<li>r = 10 cm<\/li>\n<\/ul>\n<p><strong>Result:<\/strong><\/p>\n<p>The resulting absorbed dose rate in grays per hour is then:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation-1.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-25319\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation-1.png\" alt=\"absorbed dose rate - gray - calculation\" width=\"551\" height=\"153\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation-1.png 551w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation-1-300x83.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/a><\/p>\n<p>If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The <strong>extended formula<\/strong> for the dose rate is then:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-25303\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation.png\" alt=\"absorbed dose rate - gray\" width=\"693\" height=\"158\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation.png 693w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2018\/10\/absorbed-dose-rate-gray-calculation-300x68.png 300w\" sizes=\"(max-width: 693px) 100vw, 693px\" \/><\/a><\/p>\n<\/div><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<p><strong>Radiation Protection:<\/strong><\/p>\n<ol>\n<li>Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8\/2010. ISBN-13: 978-0470131480.<\/li>\n<li>Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10\/2010. ISBN-13: 978-1441923912.<\/li>\n<li>Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4\/2013. ISBN-13: 978-3527411764.<\/li>\n<li>U.S.NRC, NUCLEAR REACTOR CONCEPTS<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.<\/li>\n<\/ol>\n<p><strong>Nuclear and Reactor Physics:<\/strong><\/p>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317<\/li>\n<li>W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467<\/li>\n<li>G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965<\/li>\n<li>Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.<\/li>\n<li>U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.<\/li>\n<li>Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.<\/li>\n<\/ol>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Absorbed Dose<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/radiation-protection\/absorbed-dose\/\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":25316,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/25326"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=25326"}],"version-history":[{"count":2,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/25326\/revisions"}],"predecessor-version":[{"id":37858,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/25326\/revisions\/37858"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/25316"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=25326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}