Question

Iodine has Half life of 8 days. If there are 200 grms of this sample. How much of iodine will remain after 32 days?

Answer 1

Answer:

32 days means 4 half lives since one half life is 8 days. That means it will be halved 4 times... so the ratio between the initial amount and the amount after 32 days will be 0.54 . There will be 2.2 grams left.

Explanation:

hope this helps u

Answer 2

Given : Half life of Iodine(I) = 8 days

            Initial amount of Iodine ($N_{0}$) = 200g

To Find: Final amount of Iodine (N) left after 32 days

Solution:

• Half life of an element is defined as the amount of time taken by it to reduce to half its initial amount due to its radioactive nature.
• For this question we will use the formula

                                         N = $N_{0}$ $e^{-λt}$

where,

               N is the final amount of I left after 32 days

               $N_{0}$ is the initial amount of I taken

               e is the base of natural logarithm

                λ is the decay constant which is equal to $\frac{ln 2}{ half life}$

         and t is the time given = 32 days

• Substituting these values into the given formula, we get

                  N = 200 × $e^{-\frac{ln 2}{8} . 32 }$

         ⇒      N = 200 × $e^{-4. ln 2}$

         ⇒      N = 200 ×   $e^{-ln 16}$                          ( a × ln x = ln $x^{a}$)

         ⇒      N = 200 × $\frac{1}{16}$                                  ( $x^{ln a}$ = a)

         ⇒      N = 12.5 g

∴ At the end of 32 days 12.5 g of Iodine will be left.