ISOTOPES & AVERAGE ATOMIC MASS Agenda P. 26-27-Average Atomic Mass (O/S) HW: P.27# 1; P.29 # 1-9 and w/s ATOMS • Each elements is made up unique atoms • The atoms of an element have identical chemical properties • All atoms of an element may have the SAME NUMBER OF ELECTRONS AND PROTONS • Some atoms of an element may may have a different number of NEUTRONS and therefore different ATOMIC MASS NUMBER Isotopes of the same element have the same chemical properties but different physical properties ( different mass). ISOTOPES • Atoms of the same element having the same number of protons in their nucleus but a different number of neutrons are isotopes of each other • The average atomic mass number shown in the periodic table is the result of an average mass based on the abundance of each isotope. • Most elements occur naturally as mixtures of isotopes, as indicated on your handout. The percentage of each isotope in the naturally occurring element on Earth is nearly always the same, no matter where the element is found. AVERAGE ATOMIC MASS • Isotopes with different mass numbers exist in a fixed ratio in a sample of an element • The percent abundance of each isotope can be determined by mass spectroscopy • This percent abundance is used to calculate the average atomic mass of the element • It is used as a weighted measure of the mass of a specific isotope AVERAGE ATOMIC MASS [A and B are isotope masses] AAM = % abundance x mass A + % abundance x mass B AVERAGE ATOMIC MASS Example: A sample of carbon has two isotopes C-12 and C-13, with C-12 comprising 98.89 % of the sample and C-13 comprising 1.11 % . Find the average atomic mass. A.A.M. = = = (0.9889)(12) + (0.0111)(13) 11.86 + 0.144 12.01 a.m.u. Therefore the average atomic mass of carbon is 12.01 u. Q- Sometimes an isotope is written without its atomic number - e.g. 35S (or S-35). Why? A- The atomic # of an element does not change. Although the number of neutrons can vary, atoms have definite numbers of protons. Example: A sample of two naturally occurring isotopes of lithium, Li-6 and Li-7 have masses of 6 u and 7 u, respectively. Which of these two occurs in greater abundance? AMM = 6.941 u ( as shown on the periodic table) Lithium-7 must be more abundant 6Li 3 p+ 3 n0 7Li 2e– 1e– 3 p+ 4 n0 2e– 1e– Every element on the periodic table has at least 2 isotopes and some elements have as many as 25 isotopes. The isotopes of hydrogen have separate names rather than being called hydrogen-1, hydrogen-2, etc. Their names are protium (H-1), deuterium (H-2), and tritium (H-3). Agenda P. 23- 29 • Radioisotopes • Half Life Definition & C-14 dating HW: Worksheets Radioisotopes • Some isotopes are stable like H-2 while other isotopes are unstable like C-14 • Unstable isotopes are called radioisotopes • Radioisotopes undergo radioactive decay resulting in the production of ionizing radiation and a more stable nucleus • Each radioisotope has a characteristic rate of decay that is known as a half-life HALF LIFE • Radioisotopes undergo radioactive decay at fixed unique rates that are characteristic for each different radioisotope • The time it takes for half (1\2) of the nuclei in a radioactive sample to decay is known as the half-life of the radioisotope • Half-lives may vary from a few seconds to many years [Po-226 has a 0.16 s half-life while Cs-142 has a 5 x 1015 a (years) half-life] Carbon dating - Uses C-14 to date organic material. - Carbon- 14 has a half-life of 5730 a. - Carbon is constantly recycled through the carbon cycle through living organisms, and the proportion of carbon - 14 remains constant. Once an organism dies, the recycling of carbon stops and C -14 starts to decay. As time goes on the remains contain fewer and fewer C -14 atoms. - By comparing the amount of C -14 in an organic sample to the amount present in living organisms, it is possible to determine the age of the organic sample. How carbon -14 is made. Uses of radioisotopes • Non living material such as rocks can be dated similarly using K -40 with a half-life of 1.3 x 109 a. • Anthropologists and geologists commonly use these techniques to date both once living artifacts as well as rocks. • Other disciplines that find these techniques useful are forensic pathologists, museum curators, art experts and art authenticators. Half Life Problems • Example Problem: Phosphorus-32 has a half-life of 14.3 days. How many mg of phosphorus-32 remain after 57.2 days if you start with 4.0 mg of the isotope? Amount of Phosphorus-32 4mg 2mg 1mg 0.5mg 0.25mg Time Elapsed 0 days have past 14.3 days have past 28.6 days have past 42.9 days have past 57.2 days have past • Another way to work problems: # of half-lives = time elapsed x ratio for half-life # of half-lives = 57.2 days x 1 half-life = 4 half-lives 14.3 days • So now we know the answer will be: 4mg x ½ x ½ x ½ x ½ = 0.25mg or 4mg x (½)4 = 0.25mg Another way to work problems: Use the following formula Af is the amount of substance left Ai is the original amount of substance t is the elapsed time t1/2 is the half-life of the substance Radioisotopes Unstable isotopes undergo radioactive decay giving off radiation and changing the composition of their nuclei. This emission of radiation from the nucleus of an atom is known as RADIOACTIVITY. There are 3 types of radiation given off by radioisotopes. 1. ALPHA particles (42He2+ , ) - the nuclei of helium atom - have 2 protons and 2 neutrons - have a 2 + charge - stopped n a few centimeters of air 2. BETA particles ( , e- ) - electrons travelling at a very high speed - have a negative charge - stopped by a thin sheet of lead or aluminum foil. 3. GAMMA rays () - do not consist of particles - a form of high energy radiation, similar to X-rays - stopped by a sheet of lead several centimeters thick or reinforced concrete.