Question

A lab technician had a sample of radioactive Americium. He knew it was one of the isotopes listed in the table below but did not know which one. The sample originally contained 0.008 g of the isotope, but 120 minutes later it contained 0.002 g.
a. How many half-lives have passed?
b. What is the half-life of the sample?
c. Which isotope did he have?

Answer 1

2 half lives. .008>.004>.002

the half life is 1 hour

he had Am-237

Answer 2

Answer: a. 2

b. 1 hour

c. Am-237

Explanation:

Half life is the time taken by a reactant to reduce to its original concentration. It is designated by the symbol $t_\frac{1}{2}$.

Formula used :

$a=\frac{a_o}{2^n}$

where,

a = amount of reactant left after n-half lives = 0.002

$a_o$ = Initial amount of the reactant = 0.008 g

n = number of half lives  = ?

Putting values in above equation, we get:

$0.002=\frac{0.008}{2^n}$

$2^n=4\\\2^n=2^2$

$n=2$

Thus two half lives have passed.

2. If two half lives have passed in 120 minutes

one half life will be passed in =$\frac{120}{2}\times 1=60 minutes$ or 1 hour

3. As half life is characteristic of a particular isotope.

Given : the half life of isotope Am-237 is 1 hour or 60 minutes. thus the isotope was Am-237.