Atoms decay by transforming protons and neutrons
into other particles. This decay process is
predictable in that we can determine how many atoms
will decay over a given period of time, we just don't
know which atoms will decay. Half-life is the
time it takes for half of the original sample of
radioactive nuclei to decay. Half-life is a
statistical model. The number of decay is not
completely regular, but on average the number of
decays for a particular isotope is consistent.

500g of X going through 6 half-lives

500 g250
g125
g62.5
g31.25
g15.625
g7.8125
g

half-life

0

1

2

3

4

5

6

7

8

fraction

remaining

1

1/2

1/4

1/8

1/16

1/32

1/64

1/128

1/256

graphing examples

This plot shows how the number of radioactive
nuclei in a sample falls with time. After 0.7 hours the original
number of 1000 active nuclei has fallen to 500. The strength of
the source has accordingly fallen in half. Of the remaining
active nuclei a further half will have decayed in the following
0.7 hours leaving only 250 and so on down to 125 after 2.1
hours. The time taken for the strength of the source to fall in
half is called the half-life and depends only on the particular
element involved and exactly how unstable it is.

Past Regents Questions

Jan 2004-47
After 32 days, 5 milligrams of an 80-milligram sample of a radioactive isotope
remains unchanged. What is the half-life of this element?
(1) 8 days (3) 16 days
(2) 2 days (4) 4 days

June 2008-50
An original sample of K-40 has a mass of 25.00 grams. After 3.9 × 10^{9}years,
3.125 grams of the original sample remains unchanged. What
is the half-life of K-40?
(1) 1.3 × 10^{9}y (3)
3.9 × 10^{9}y
(2) 2.6 × 10^{9}y (4)
1.2 × 10^{10 }y

June 2006-49
What is the half-life of sodium-25 if 1.00 gram of a 16.00-gram sample of
sodium-25 remains unchanged after 237 seconds?
(1) 47.4 s (3) 79.0 s
(2) 59.3 s (4) 118 s

Jun 2005-29
What is the half-life and decay mode of Rn-222?
(1) 1.91 days and alpha decay
(2) 1.91 days and beta decay
(3) 3.82 days and alpha decay
(4) 3.82 days and beta decay