Answer
398.7k+ views
Hint: We know that for a reaction to take place, the mass number and atomic number on the product side must be equal to that on the reactant side. So, they compared the equations for mass number and atomic number on both sides, the value of alpha and beta can be calculated.
Complete step by step solution
The given reaction is:
$ _{92}{{\text{U}}^{238}}{{\to }_{82}}\text{P}{{\text{b}}^{214}}+\text{a }{{\text{ }}_{2}}\text{H}{{\text{e}}^{4}}+\text{b }{{\text{ }}_{-1}}{{\text{e}}^{0}} $
We assume that “a” number of (alpha) $ \alpha $ particles and “b” number of $ \beta $ (beta) particles are emitted.
Now, we know that for every reaction, the mass number and atomic number must be conserved, that is, mass number and atomic number on the product side must be equal to that on the reactant side.
Firstly, on equating the mass numbers on both sides, we get
$ \begin{align}
& 238=214+4\text{ a}+0 \\
& 238=214+4\text{ a} \\
& \text{ 4 a}=24 \\
& \text{ a}=\dfrac{24}{4} \\
& \text{ a}=6 \\
\end{align} $
Therefore, 6 alpha particles are emitted
Now, on equating the atomic numbers on both sides, we get:
$ \begin{align}
& 92=82+2\text{ a}-\text{b} \\
& \text{92}-\text{82=2 a}-\text{b} \\
& \text{92}-82=2\times 6-\text{b} \\
\end{align} $
$ \begin{align}
& \text{92}-82-12=-\text{b} \\
& -\text{b}=-2 \\
& \text{b=2} \\
\end{align} $
Therefore, 2 beta particles are emitted.
So, the correct option is (A).
Note
Alpha particles consist of 2 protons and 2 neutrons bound together into a particle identical to $ \text{H}{{\text{e}}^{4}} $ nucleus.
They are generally produced in the proven of alpha decay, The electric charge is $ +2\text{ e} $ , mass is $ 6\cdot 6446\times {{10}^{-27}}\text{ kg} $ and spin=0.
Beta particles are a high energy, high speed electron or positron which is emitted by the radioactive decays of an atomic nucleus during the process of beta decay. It has charge $ -1 $ ,Mass $ =\dfrac{1}{2000}\text{ th} $ of a proton and spin $ =\dfrac{1}{2} $
Complete step by step solution
The given reaction is:
$ _{92}{{\text{U}}^{238}}{{\to }_{82}}\text{P}{{\text{b}}^{214}}+\text{a }{{\text{ }}_{2}}\text{H}{{\text{e}}^{4}}+\text{b }{{\text{ }}_{-1}}{{\text{e}}^{0}} $
We assume that “a” number of (alpha) $ \alpha $ particles and “b” number of $ \beta $ (beta) particles are emitted.
Now, we know that for every reaction, the mass number and atomic number must be conserved, that is, mass number and atomic number on the product side must be equal to that on the reactant side.
Firstly, on equating the mass numbers on both sides, we get
$ \begin{align}
& 238=214+4\text{ a}+0 \\
& 238=214+4\text{ a} \\
& \text{ 4 a}=24 \\
& \text{ a}=\dfrac{24}{4} \\
& \text{ a}=6 \\
\end{align} $
Therefore, 6 alpha particles are emitted
Now, on equating the atomic numbers on both sides, we get:
$ \begin{align}
& 92=82+2\text{ a}-\text{b} \\
& \text{92}-\text{82=2 a}-\text{b} \\
& \text{92}-82=2\times 6-\text{b} \\
\end{align} $
$ \begin{align}
& \text{92}-82-12=-\text{b} \\
& -\text{b}=-2 \\
& \text{b=2} \\
\end{align} $
Therefore, 2 beta particles are emitted.
So, the correct option is (A).
Note
Alpha particles consist of 2 protons and 2 neutrons bound together into a particle identical to $ \text{H}{{\text{e}}^{4}} $ nucleus.
They are generally produced in the proven of alpha decay, The electric charge is $ +2\text{ e} $ , mass is $ 6\cdot 6446\times {{10}^{-27}}\text{ kg} $ and spin=0.
Beta particles are a high energy, high speed electron or positron which is emitted by the radioactive decays of an atomic nucleus during the process of beta decay. It has charge $ -1 $ ,Mass $ =\dfrac{1}{2000}\text{ th} $ of a proton and spin $ =\dfrac{1}{2} $
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)