Answer
443.7k+ views
Hint: The energy of a neutron is given, and we can calculate the linear momentum associated with the neutron from the energy given and the mass given in the problem. If d is the distance of closest approach, then the linear momentum times the distance of closest approach gives the relative angular momentum of the neutron with respect to the proton.
Formula Used:
The linear momentum associated with a body which has a kinetic energy E and mass m is given by the formula,
$p=\sqrt{2mE}$
Angular momentum of a body of mass m, moving with a linear velocity v at a perpendicular distance r from the origin is given by,
L=mvr
Complete step by step answer:
In the question, it is given that the energy or the kinetic energy of a neutron is $1MeV$ and also the mass of the neutron is given $1.6\times {{10}^{-27}}kg$. So, from these factors, we can calculate the linear momentum associated with the neutron using the formula,
$p=\sqrt{2{{m}_{p}}E}$
Where ${{m}_{p}}$ is the mass of the proton. We can substitute the values in the above equation to get,
$p=\sqrt{2\times 1.6\times {{10}^{-27}}kg\times 1\times {{10}^{6}}eV}$
$p=\sqrt{2\times 1.6\times {{10}^{-27}}kg\times \left( 1\times {{10}^{6}}\times 1.6\times {{10}^{-19}} \right)J}$
$\therefore p=2.26\times {{10}^{-20}}kgm{{s}^{-1}}$
So, we now have the linear momentum associated with the neutron. The relative angular momentum of the neutron with respect to the proton can be represented as, (we can take the position of the proton as the origin)
Relative angular momentum=mvd=pd
Where d is the distance of the closest approach, p is the linear momentum of the neutron. We are given that the relative angular momentum of the neutron with the proton is ${{10}^{-35}}Js$, So we can write,
${{10}^{-35}}Js=pd$
$\Rightarrow {{10}^{-35}}Js=\left( 2.26\times {{10}^{-20}}kgm{{s}^{-1}} \right)d$
$\Rightarrow d=\dfrac{{{10}^{-35}}Js}{2.26\times {{10}^{-20}}kgm{{s}^{-1}}}$
$\therefore d=0.44fm$
So, the distance of the closest approach is 0.44 fm.
So, the answer to the question is option (D).
Note: In physics, angular momentum is the analogue of linear momentum for a rotating body. It is a pseudovector which means it transforms like a vector but is not really a vector. In three dimension it can be represented by the formula, \[\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}\], where L is the angular momentum of the body, r is the position vector from the origin and p is the linear momentum of the body.
Conservation of Angular Momentum: When no external torque acts on a rotating body or system executing a uniform rotational motion, then the angular momentum of the body is said to be conserved. Which means that the angular momentum does not change with time. The theorem is analogous to Newton’s third law.
The angular momentum of an extended body can be expressed as the product of the moment of inertia of the body and its angular velocity.
Formula Used:
The linear momentum associated with a body which has a kinetic energy E and mass m is given by the formula,
$p=\sqrt{2mE}$
Angular momentum of a body of mass m, moving with a linear velocity v at a perpendicular distance r from the origin is given by,
L=mvr
Complete step by step answer:
In the question, it is given that the energy or the kinetic energy of a neutron is $1MeV$ and also the mass of the neutron is given $1.6\times {{10}^{-27}}kg$. So, from these factors, we can calculate the linear momentum associated with the neutron using the formula,
$p=\sqrt{2{{m}_{p}}E}$
Where ${{m}_{p}}$ is the mass of the proton. We can substitute the values in the above equation to get,
$p=\sqrt{2\times 1.6\times {{10}^{-27}}kg\times 1\times {{10}^{6}}eV}$
$p=\sqrt{2\times 1.6\times {{10}^{-27}}kg\times \left( 1\times {{10}^{6}}\times 1.6\times {{10}^{-19}} \right)J}$
$\therefore p=2.26\times {{10}^{-20}}kgm{{s}^{-1}}$
So, we now have the linear momentum associated with the neutron. The relative angular momentum of the neutron with respect to the proton can be represented as, (we can take the position of the proton as the origin)
Relative angular momentum=mvd=pd
Where d is the distance of the closest approach, p is the linear momentum of the neutron. We are given that the relative angular momentum of the neutron with the proton is ${{10}^{-35}}Js$, So we can write,
${{10}^{-35}}Js=pd$
$\Rightarrow {{10}^{-35}}Js=\left( 2.26\times {{10}^{-20}}kgm{{s}^{-1}} \right)d$
$\Rightarrow d=\dfrac{{{10}^{-35}}Js}{2.26\times {{10}^{-20}}kgm{{s}^{-1}}}$
$\therefore d=0.44fm$
So, the distance of the closest approach is 0.44 fm.
So, the answer to the question is option (D).
Note: In physics, angular momentum is the analogue of linear momentum for a rotating body. It is a pseudovector which means it transforms like a vector but is not really a vector. In three dimension it can be represented by the formula, \[\overrightarrow{L}=\overrightarrow{r}\times \overrightarrow{p}\], where L is the angular momentum of the body, r is the position vector from the origin and p is the linear momentum of the body.
Conservation of Angular Momentum: When no external torque acts on a rotating body or system executing a uniform rotational motion, then the angular momentum of the body is said to be conserved. Which means that the angular momentum does not change with time. The theorem is analogous to Newton’s third law.
The angular momentum of an extended body can be expressed as the product of the moment of inertia of the body and its angular velocity.
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)