Question

According to Figure 13-2, if 25 percent of the parent material remains in a rock sample, how many half-lives have occurred?

Answer 1

2 half lives. A half life is when a substance is broken down by half. 100% -> 50% etc.

Answer 2

Answer: Number of half lives occurred 2.

Step-by-step explanation:

Let the initial concentration be x

Concentration left=25 % of the x=
`x(25)/(100)=(x)/(4)`

To calculate the number of half lives, we use the formula:

`a=(a_o)/(2^n)`..(1)

where,

a = amount of reactant left after n-half lives = 0.0495 moles

`a_o` = Initial amount of the reactant = 0.7924 moles

n = number of half lives

`(x)/(4)=(x)/(2^n)`

taking log both sides

`\logx-\log4=\logx-n\log2`

`\log4=n\log2`

`\log(2)^2=2\log2=n\log2`

n = 2

Number of half lives occurred 2.