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

Explanation:

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

              N = $N_{0} (\frac{1}{2})^{l}$

where,     $N_{0}$ = number of initial particles

                              l = number of half lives

As it is given that number of initial particles is $128 \times 10^{10}$ and number of half-lives is 3.

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

               N = $N_{0} (\frac{1}{2})^{l}$

                    = $128 \times 10^{10}(\frac{1}{2})^{3}$

                    = $16 \times 10^{10}$

or,                    $1.6 \times 10^{11}$

Thus, we can conclude that $1.6 \times 10^{11}$ particles of radioactive nuclei remain in the given sample.

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

particles