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

Answer:

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;

N_t = N_o X (0.5)^{Number of half-lives}

Where:

N_t = Amount of radioisotope remaining

N_o = Original amount of radioisotope

Number of half-lives = Time ÷ Half-life

N_o = 100%

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