half-life - drbperiodbsem2

P. 26-27-Average Atomic Mass (O/S)
P.27# 1; P.29 # 1-9 and w/s
• Each elements is made up unique atoms
• The atoms of an element have identical chemical
• All atoms of an element may have the SAME
• Some atoms of an element may may have a different
number of NEUTRONS and therefore different
Isotopes of the same element have the same chemical
properties but different physical properties ( different
• 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.
• 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
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)
+ 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
AMM = 6.941 u ( as shown on the periodic table)
Lithium-7 must be more abundant
3 p+
3 n0
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
P. 23- 29
• Radioisotopes
• Half Life Definition & C-14 dating
HW: Worksheets
• 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
• Radioisotopes undergo radioactive decay at fixed
unique rates that are characteristic for each different
• 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
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
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
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
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
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.