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# Half life of a radioactive element is 50 days. How many half life it will take to become 12.5% of the original amount?

By Suman Patra

The half-life of a radioisotope is the time required for half the atoms in a given sample to undergo radioactive, or nuclear, decay.

Initially, at time t = 0, the sample is 100%.

After 50 days, only half the original amount of element will remain:

½ x 100% = 50%

After another 50 days, only half of this amount of will remain:

½ x 50% = 25%

After another 50 days, only half of this amount of strontium will remain:

½ x 25% = 12.5%

This can be represented in the form of a table:

 Number of Half-lives Time (Days) % of Radioactive element remaining % of Radioactive element decayed 0 0 100 0 1 50 50 50 2 100 25 75 3 150 12.5 87.5

Hence, we can see that there are 3 half lives required for the element to become 12.5% of the original amount.

In case you need to calculate the percentage remaining after some other number of days or years or hours, you can use the formula;

Nt = No X (0.5)Number of half-lives

Where:

Nt = Amount of radioisotope remaining

No = Original amount of radioisotope

Number of half-lives = Time ÷ Half-life

No = 100%

(Time is the number of days or years or hours given).

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