Answer
64.8k+ views
Hint: To answer this question we should be implementing the formula of half-life. Once we find an answer we can use the formula which develops the relationship between the remaining amount and the original amount of the radioactive material. This formula will give us the required amount as an answer.
Complete step by step answer:
The time that is given in the question is 5 minutes. This can be written as t = 5 minutes or $t = 5 \times 60\operatorname{s} = 300s$.
So now we can write that the number of half-lives is n or we can say
$n = \dfrac{t}{{{t_{1/2}}}}$
Put the values in the above equation to get:
$\dfrac{{300}}{{100}} = 3$
Now we have to find the relationship between the remaining amount which is N and the initial amount which is \[{N_0}\].
The formula to find the relationship between N and \[{N_0}\]is given by:
\[N = {N_0}{\left( {\dfrac{1}{2}} \right)^n}\]
Solving the above relation, we get that:
\[N = \dfrac{{{N_0}}}{8},{N_0} = 8gm\]
So we can say that after 5 minutes the remaining amount or N will be 1 gm.
So, the correct answer is Option A.
Note: In this question we have come across the term half-life. For the better understanding we need to know the meaning of the term half-life. By half-life we mean the time that is required for any specific quantity to reduce to half of the initial value of itself. The half-life actually signifies how the atoms that form the quantity are unstable and they undergo a radioactive decay. From the value of the half-life we can find out the stability of the atoms forming a specific quantity.
Complete step by step answer:
The time that is given in the question is 5 minutes. This can be written as t = 5 minutes or $t = 5 \times 60\operatorname{s} = 300s$.
So now we can write that the number of half-lives is n or we can say
$n = \dfrac{t}{{{t_{1/2}}}}$
Put the values in the above equation to get:
$\dfrac{{300}}{{100}} = 3$
Now we have to find the relationship between the remaining amount which is N and the initial amount which is \[{N_0}\].
The formula to find the relationship between N and \[{N_0}\]is given by:
\[N = {N_0}{\left( {\dfrac{1}{2}} \right)^n}\]
Solving the above relation, we get that:
\[N = \dfrac{{{N_0}}}{8},{N_0} = 8gm\]
So we can say that after 5 minutes the remaining amount or N will be 1 gm.
So, the correct answer is Option A.
Note: In this question we have come across the term half-life. For the better understanding we need to know the meaning of the term half-life. By half-life we mean the time that is required for any specific quantity to reduce to half of the initial value of itself. The half-life actually signifies how the atoms that form the quantity are unstable and they undergo a radioactive decay. From the value of the half-life we can find out the stability of the atoms forming a specific quantity.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)