Question

Initially, a particular sample has a total mass of 200 grams and contains 128 x 1010 radioactive nuclei. These radioactive nuclei have a half life of 1 hour. (a) After 3 hours, how many of these radioactive nuclei remain in the sample (that is, how many have not yet experienced a radioactive decay)

Answer 1

Step-by-step explanation:

Formula to calculate how many particles are left is as follows.

N =
`N_(0) ((1)/(2)</p><p>)^(l)`

where,
`N_(0)` = number of initial particles

l = number of half lives

As it is given that number of initial particles is
`128 * 10^(10)` and number of half-lives is 3.

Hence, putting the given values into the above equation as follows.

N =
`N_(0) ((1)/(2))^(l)`

=
`128 * 10^(10)((1)/(2))^(3)`

=
`16 * 10^(10)`

or,
`1.6 * 10^(11)`

Thus, we can conclude that
`1.6 * 10^(11)` particles of radioactive nuclei remain in the given sample.

In five hours we've gone through 5 half lives so the answer is:

particles