Everything Science Grade 11

CHAPTER 4. ATOMICNUCLEI 4.5

Example 2: Half-life 1

QUESTION

A 100 g sample of Cs− 137 is allowed to decay. Calculate the mass of Cs− 137 that will be

left after 90 years

SOLUTION

Step 1 : You need to know thehalf-life of Cs− 137

The half-life of Cs− 137 is 30 years.

Step 2 : Determine how many times the quantity of sample will be halved in 90years.

If the half-life of Cs− 137 is 30 years, and the sample is left to decay for 90years,

then the number of times the quantity of samplewill be halved is^9030 = 3.

Step 3 : Calculate the quantitythat will be left by halving the mass of Cs− 137 three

times

1. After 30 years, the mass left is 100 g×^12 = 50 g


2. After 60 years, the mass left is 50 g×^12 = 25 g


3. After 90 years, the mass left is 25 g×^12 = 12. 5 g
   Note that a quicker wayto do this calculation isas follows:
   Mass left after 90 years = (^12 )^3 × 100 g = 12. 5 g (The exponent is the
   number of times the quantity is halved)

Example 3: Half-life II

QUESTION

An 80 g sample of Po− 212 decays until only 10 gis left. How long did ittake for this decay

to take place?

SOLUTION

Step 1 : Calculate the fraction of the original sample that is left after decay

Fraction remaining =^1080 g g=^18

Step 2 : Calculate how many half-life periods of decay(x) must have taken place for^18

of the original sample to be left