Question

After five half-lives, what will be the fraction of the initial substance?
A. \[{(\dfrac{1}{2})^{10}} \\ \]
B. \[{(\dfrac{1}{2})^5} \\ \]
C. \[{(\dfrac{1}{2})^4} \\ \]
D. \[{(\dfrac{1}{2})^3}\]

Answer 1

Hint: As per the question, we need to find the fraction of the initial substance after five half-lives. According to the question, the number of half-life is 5 days. Then the fraction can be calculated by using the below formula.

Formula Used
\[\dfrac{N}{{{N_0}}}\]= \[{(\dfrac{1}{2})^n}\]
Here, \[{N_0}\] is the amount of substance that will initially decay and \[N\] is the quantity that still remains.

Complete step by step solution:
Half-life describes the amount of time that it takes for half of a specific sample to react i.e it indicates the time that a certain quantity needs to decrease its initial value to half. Half-life is the time interval where the mass of a radioactive element or the number of its atoms, is decreased to half its initial value is known as the half-life of that substance.

It is one of the common terminologies used in Physics. It is also known as the Half-Life Period. This term is used to define the radioactive decay of a certain sample or element within a specified period. Though, the various kinds of decay processes, particularly non-exponential and exponential decay are defined by using this concept.

Given, Number of half-lives n=5
We know that,
\[\dfrac{N}{{{N_o}}}\]= \[{(\dfrac{1}{2})^n}\]
\[\therefore {(\dfrac{1}{2})^n}\]= \[{(\dfrac{1}{2})^5}\]
Therefore, the fraction is \[{(\dfrac{1}{2})^5}\].

Therefore the correct answer is option B.

Note: In this type of question, we need to find the fraction of the initial substance. Therefore, while solving this problem, the students must keep this in mind. So, they can solve it easily.