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?

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

A- The atomic # of an element does not change. Although the number of neutrons can vary, atoms have definite numbers of protons.

3 p+

3 n02e– 1e–

6Li 7Li

3 p+

4 n02e– 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 datingHW: 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

Time Elapsed

4mg 0 days have past2mg 14.3 days have past 1mg 28.6 days have past0.5mg 42.9 days have past0.25mg 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

Af is the amount of substance leftAi is the original amount of substancet is the elapsed timet1/2 is the half-life of the substance

Another way to work problems: Use the following formula

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 (4

2He2+ , )

- 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.