- Heavy (222 vs. ~40 for air)
- #2 cause of lung cancer in the us
- emitted from radioactive rocks (e.g. granite)
- in cigarette smoke
- alpha emitter (see below)
4 types of radiation:
alpha: Helium nucleus He4/2 (charged, heavy)-stopped by skin, paper
beta: fast electron e- (charged, small)-stopped by foil
gamma: high energy photon, like light-stopped by lead
neutron: just a neutron n1/0 (heavy, no charge)-stopped by lots of lead and concrete
Review Isotopes:
Radon is 222/86: how many n, p and e?
How many for C 14/6?
Exponential decay and growth: decay for radioactive stuff, growth for populations and bacteria
Decay formula: At = Ao (0.5)^n
Growth formula: At = Ao (2)^n
At = amount some time later, time t
Ao = starting amount
n = number of half lives (t1/2) or doubling times (t2)
We'll use M&Ms as our "atoms" for this:
- pour out 32 M&Ms on a plate
- drop into a shaker, shake, pour out on the plate
- remove the ones with the M&M label facing up
- count the remainder
- repeat
- graph number of M&Ms (y) number of turns (x)
Questions:
- Does the number ever really get to zero in real live atoms?
- What is the change in atoms at each turn?
- How is this related to the amount of atoms left?
Problems:
- 64 grams of C14/6 with half life of about 5000 years decays.
- How much is left after 5000 years?
- 15,000 years?
- 30,000 years?
- Sr90/38 has a half life of about 30 years. If Ao is 200 grams,
- how much is left after 60 years?
- 120 years?
- 45 years?
Setup for each problem:
- find n (60/30 = 2)
- find Ao (200 grams)
- At = 200(0.5)^2 = 50 grams
n.b. 45 grams is not a whole number of half lives
so what? just use the number to get 70 grams (try this)
Exponential growth:
Same deal as with decay, only we use 2 instead of 0.5
Decay formula: At = Ao (0.5)^n
Growth formula: At = Ao (2)^n
n is called t2 or the doubling time (you may have seen this in AP bio)
Example: If bacteria population doubles every 6 hours, and Ao is 1000 bacteria, how many after 24 hours?
24/6 = 4 = n
At = 1000(2)^4 = 16,000 bacteria
This works for people, viruses, rhinos, even capybaras...
One reason antibiotics and antivirals attack the reproductive cycle, not existing viruses.
n.b. this depends on two things:
RATE: the reproductive or decay rate
BASE: how much you start with
Exponential Growth Lab:
- Start with 4 M&Ms, double until 32, graph
- On the same graph, repeat starting with 8 M&Ms
- What is the change in M&Ms at each turn?
- which graph has the steeper slope?
- how would birth control change t2?
- why did China have a one child policy had between 1980 and 2015?
Examples: (numbers are grossly estimated for comparison)
Each country starts with about 30 million in this example:
How many in each case after 42 years?
Canada t2=21 years
Nigeria t2=7 years
Japan t2 = -7 years (?)
Rule of 70
Countries use growth rate instead of t2
If growth rate is 7%, then 70/7 means 10 years is t2
if growth rate is 14% then 70/14 means 5 years for t2
if growth rate is 3.5% then 70/3.5 means 20 years for t2
Populations depends on BASE and RATE