Transcript Half-Life - Montville.net

Unit: Nuclear Chemistry
Half-Life
After today you will be able to…
• Identify the factor that nuclear
stability is dependent on.
• Calculate the half-life for a given
radioisotope.
• Calculate how much of a
radioisotope remains after a
given amount of time.
Nuclear Stability
• Close to 2,000 different nuclei are
known.
• Approximately 260 are stable and
do not decay or change with time.
• The stability (resistance to change)
depends on its neutron:proton
ratio.
Nuclear Stability
• Plotting a graph of
number of
neutrons vs.
number of protons
for each element
results in a region
called the band of
stability.
Nuclear Stability
• For elements with
low atomic
numbers (below
20) the ratio of
neutrons:protons
is about 1.
12
–Example: 6 C
(6n/6p = 1)
Nuclear Stability
• For elements with
higher atomic numbers,
stable nuclei have more
neutrons than protons.
The ratio of n:p is
closer to 1.5 for these
heavier elements.
– Example: 206
82
Pb
124n/82p = approx. 1.5
Nuclear Stability
• The neutron:proton
ratio iswhy
Ever wonder
important because
it
some atomic
masses
determines listed
the type
of Periodic
decay
on the
that occurs.Table have ( ) around
• All nuclei that
have
an atomic
them?
Because
their
number greater
thanmasses
83 areare
atomic
radioactive. estimated due to
radioactive decay!
Half-Life
Half-life: (t1/2) the time required for half of
the nuclei of a radioisotope sample to decay
to products.
• Example: If you have 20 atoms of Radon222, the half life is ~4 days. How many
atoms remain at the end of two half lives?
0 t1/2
20 atoms
initially
4 days
1 t1/2
10 atoms
8 days
2 t1/2
5 atoms
remain
Half-Life
• We can
represent halflife graphically
as well.
—Example:
Carbon-14
However, very seldom do we
count atoms. Therefore it is
more appropriate to
calculate amount that
remains in terms of mass.
Half-Life
• Example: Carbon-14 emits beta radiation and
decays with a half-life (t1/2) of 5730 years.
Assume you start with a mass of 2.00x10-12g of
carbon-14.
a.How long is three half-lives?
b.How many grams of the isotope remain
at the end of three half-lives?
a. 3(5730) = 17,190 years
b. 2.00x10-12g x 1/2 x 1/2 x 1/2 = 2.5x10-13g
Half-Life
b. How many grams of the isotope remain at the
end of three half-lives?
Alternatively, part b can also be calculated like this:
0 t1/2
2.00x10-12g
initially
x 1/2
1 t1/2
1.00x10-12g
x 1/2
2 t1/2
x 1/2
5.00x10-13g
3 t1/2
2.50x10-13g
remains
Half-Life
• Example: Manganese-56 is a beta emitter with
a half-life of 2.6 hours.
a. How many half-lives did the sample go
through at the end of 10.4 hours?
b. What is the mass of maganese-56 in a 1.0mg
sample of the isotope at the end of
10.4 hours?
a. 10.4 h/2.6 h = 4 half-lives
b. 1.0mg x 1/2 x 1/2 x 1/2 x 1/2 = 0.063 mg
Questions?
Complete and turn in
the exit ticket.