# Question #39370

##### 1 Answer

#### Explanation:

You know that the **nuclear half-life** of a radioactive nuclide, **half** of an initial sample of said to nuclide to undergo radioactive decay.

This means that **with every passing half-life**, the mass of the sample gets reduced by **half**.

If you take

#A_t = A_0 * (1/2)^color(red)(n)#

Here

#A_t# is the mass of the sample thatremains undecayedafter a period of time#t# #color(red)(n)# represents thenumber of half-livesthat pass in a given time period#t#

In your case, you know that

#t_"1.2" = "3 hours"#

You also know that the **total time** that passes is equal to

#"1 day = 24 hours"#

You can thus say that you have

#color(red)(n) = (24 color(red)(cancel(color(black)("hours"))))/(3color(red)(cancel(color(black)("hours")))) = color(red)(8) -># this means thateight half-livespass in a#"24-hour"# period.

Therefore, the mass of the sample that remains undecayed is equal to

#A_t = A_0 * (1/2)^color(red)(8)#

#A_t = A_0 * 1/256#

To find the fraction that remains undecayed, simply divide the amount that remains undecayed by the initial amount

#A_t/A_0 = (color(red)(cancel(color(black)(A_0))) * 1/256)/color(red)(cancel(color(black)(A_0))) = 1/256#