Answer
64.8k+ views
Hint - To solve this question, first we have to understand the term half-life and then we will learn about the decaying process and its terms. Lastly, we will be calculating the answer with the help of the half-life formula.
Half-life is defined as the time required for a quantity of substance to reduce to half of its initial value.Commonly used to describe how spontaneously unstable atoms undergo, or how long stable atoms survive, radioactive decay.
Complete answer:
> Radioactive decay – Radioactive decay (also known as nuclear decay) is defined as the spontaneous breakdown of an atomic nucleus resulting in the release of energy and matter from the nucleus. A material that contains an unstable nuclei is said to be radioactive.
> It has three types which are alpha, decay, gamma decay and beta decay. Each one involves the emission of one or more photons (or particles).
Now let us Calculate our answer with the half-life formula –
\[N\left( t \right) = {N_0}{\left( {\dfrac{1}{2}} \right)^{\dfrac{t}{{{t_{\dfrac{1}{2}}}}}}}\]
$N\left( t \right) = $ quantity of the substance remaining
${N_0} = $ initial quantity of the substance
$t = $ time elapsed
${t_{\dfrac{1}{2}}} = $ half-life of the substance
$n = \dfrac{{total\,time}}{{half - life\,period}} = \dfrac{{90}}{{30}} = 3$
$N = {N_0} \times {\left( {\dfrac{1}{2}} \right)^n}$
$ = 600 \times {\left( {\dfrac{1}{2}} \right)^3}$
$ = \dfrac{{600}}{8}$
$ = 75$ atoms
So, the correct answer is option C. 75 atoms
Note – Radioactive decay is random (i.e. stochastic) at the single atom level. According to the quantum theory, it is impossible to predict the decay time of a particular atom, regardless of its existence. However, when we talk about a significant number of identical atoms, the overall decay rate can be expressed by decay constant or as half-life.
Half-life is defined as the time required for a quantity of substance to reduce to half of its initial value.Commonly used to describe how spontaneously unstable atoms undergo, or how long stable atoms survive, radioactive decay.
Complete answer:
> Radioactive decay – Radioactive decay (also known as nuclear decay) is defined as the spontaneous breakdown of an atomic nucleus resulting in the release of energy and matter from the nucleus. A material that contains an unstable nuclei is said to be radioactive.
> It has three types which are alpha, decay, gamma decay and beta decay. Each one involves the emission of one or more photons (or particles).
Now let us Calculate our answer with the half-life formula –
\[N\left( t \right) = {N_0}{\left( {\dfrac{1}{2}} \right)^{\dfrac{t}{{{t_{\dfrac{1}{2}}}}}}}\]
$N\left( t \right) = $ quantity of the substance remaining
${N_0} = $ initial quantity of the substance
$t = $ time elapsed
${t_{\dfrac{1}{2}}} = $ half-life of the substance
$n = \dfrac{{total\,time}}{{half - life\,period}} = \dfrac{{90}}{{30}} = 3$
$N = {N_0} \times {\left( {\dfrac{1}{2}} \right)^n}$
$ = 600 \times {\left( {\dfrac{1}{2}} \right)^3}$
$ = \dfrac{{600}}{8}$
$ = 75$ atoms
So, the correct answer is option C. 75 atoms
Note – Radioactive decay is random (i.e. stochastic) at the single atom level. According to the quantum theory, it is impossible to predict the decay time of a particular atom, regardless of its existence. However, when we talk about a significant number of identical atoms, the overall decay rate can be expressed by decay constant or as half-life.
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
Electric field due to uniformly charged sphere class 12 physics 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)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
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)
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)