The half-life of a radio active element is 5 years. The fraction of the radioactive substance that remains after 20 years is

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Q: 96 (IAS/1994)
The half-life of a radio active element is 5 years. The fraction of the radioactive substance that remains after 20 years is

question_subject: 

Science

question_exam: 

IAS

stats: 

0,54,74,11,41,22,54

keywords: 

{'radioactive substance': [0, 1, 1, 0], 'years': [1, 0, 0, 2], 'radio': [0, 1, 0, 3], 'active element': [0, 1, 0, 0], 'fraction': [0, 1, 0, 0]}

The half-life of a radioactive element is the time it takes for half of the radioactive substance to decay.

Given that the half-life of the radioactive element is 5 years, we can determine the fraction of the substance that remains after a certain number of years by using the concept of half-life decay.

After n half-lives, the fraction remaining can be calculated as (1/2)^n.

In this case, we want to calculate the fraction remaining after 20 years, which is equivalent to 20/5 = 4 half-lives.

Plugging in n = 4 into the equation, we get:

(1/2)^4 = 1/16

Therefore, after 20 years, the fraction of the radioactive substance that remains is 1/16.

So, the correct answer is 1/16.