Question

Use the following half-life graph to answer the following question:

A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625
How many half-lives occur during 6.0 minutes?
1
3
6
12

Answer 1

Answer: 6

Step-by-step explanation:

This is a type of radioactive decay and all the radioactive process follow first order kinetics.

Half life is the time taken for an radioactive substance to decompose to half of its original value.

Now, to calculate the number of half lives, we use the formula:

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

where,

a = amount of reactant left after 6 minutes =
`(1.5625)/(2)=0.78125`

`a_o` = Initial amount of the reactant = 50

n = number of half lives = ?

Putting values in above equation, we get:

`0.78125=(50)/(2^n)`

`2^n=64`

Taking log on both sides, we get

`n\log2=\log(64)\\n=6`

Thus 6 half lives occur during 6 minutes.

Answer 2

6 half-lives occur during the 6.0 minutes.

In the graph, it was shown that the half-life started in the 50 grams point. And in every minute, one half-life occurs, that will give us a total of 6 half-lives within 6.0 minutes time.