Question

A has a half life of 5 years. Find the amount of life left after 15 years.

• A. \(\frac{1}{8}\) of initial value
• B. \(\frac{7}{8}\) of initial value
• C. \(\frac{1}{4}\) of initial value
• D. \(\frac{3}{4}\) of initial value

Answer 1

The Correct Option is A

If the half-life of substance A is 5 years, then after 5 years, the amount of substance A remaining will be half of its initial amount. 
After another 5 years (i.e. 10 years in total), the amount of substance A remaining will be half of the amount remaining after 5 years, or one quarter of the initial amount.
After another 5 years (i.e. 15 years in total), the amount of substance A remaining will be half of the amount remaining after 10 years, or one eighth of the initial amount. 
Therefore, the answer is \(\frac{1}{8}\) of the initial value.
So, the correct answer is (A) : \(\frac{1}{8}\) of initial value.
 

Answer 2

The correct answer is (A) : \(\frac{1}{8}\) of initial value
A substance has a half-life of 5 years.
The number of half life periods in 15 years\(=\frac{15}{5}=3\)
The relation used is :
\(A_t=\frac{A_∘}{2^n}\)
Here, n is number of half life periods.
\(A_{15}\ \ years=\frac{1}{2^3}=\frac{1}{8}\)
The amount of A left after 15 years is \(\frac{1}{8}\) of initial value.