Class 11 Exam > Class 11 Questions > When an electron of charge e and mass m moves...
Start Learning for Free
When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]
- a)Ze2/r
- b)-Ze2/r
- c)Ze-2/r
- d)mv2/r
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
When an electron of charge e and mass m moves with a velocity v about ...
P.E. = work done 
Most Upvoted Answer
When an electron of charge e and mass m moves with a velocity v about ...
Explanation:
The potential energy of an electron in a circular orbit of radius r around a nucleus of charge Ze can be calculated using the Coulomb's law of electrostatics. The Coulomb's law states that the force between two charges q1 and q2 separated by a distance r is given by:
F = (1/4πε0) * (q1q2/r^2)
where ε0 is the permittivity of free space.
When an electron moves in a circular orbit around a nucleus of charge Ze, the electrostatic force between the electron and the nucleus provides the necessary centripetal force to keep the electron in its orbit. The magnitude of the electrostatic force is given by:
F = (1/4πε0) * (eZe/r^2)
where e is the charge of the electron and m is its mass.
The centripetal force required to keep the electron in its circular orbit is given by:
F = mv^2/r
where v is the velocity of the electron.
Setting these two forces equal to each other, we get:
m v^2/r = (1/4πε0) * (eZe/r^2)
Multiplying both sides by r, we get:
mv^2 = (1/4πε0) * (eZe/r)
The potential energy of the electron in the circular orbit is given by the work done by the electrostatic force in bringing the electron from infinity to the orbit. This can be calculated using the formula:
U = -∫∞r F.dr
where U is the potential energy, F is the electrostatic force, and r is the distance between the electron and the nucleus.
Integrating the above expression, we get:
U = (-1/4πε0) * (eZe/r)
Therefore, the potential energy of the electron in a circular orbit of radius r around a nucleus of charge Ze is given by:
U = - (1/4πε0) * (eZe/r)
which is option B.
The potential energy of an electron in a circular orbit of radius r around a nucleus of charge Ze can be calculated using the Coulomb's law of electrostatics. The Coulomb's law states that the force between two charges q1 and q2 separated by a distance r is given by:
F = (1/4πε0) * (q1q2/r^2)
where ε0 is the permittivity of free space.
When an electron moves in a circular orbit around a nucleus of charge Ze, the electrostatic force between the electron and the nucleus provides the necessary centripetal force to keep the electron in its orbit. The magnitude of the electrostatic force is given by:
F = (1/4πε0) * (eZe/r^2)
where e is the charge of the electron and m is its mass.
The centripetal force required to keep the electron in its circular orbit is given by:
F = mv^2/r
where v is the velocity of the electron.
Setting these two forces equal to each other, we get:
m v^2/r = (1/4πε0) * (eZe/r^2)
Multiplying both sides by r, we get:
mv^2 = (1/4πε0) * (eZe/r)
The potential energy of the electron in the circular orbit is given by the work done by the electrostatic force in bringing the electron from infinity to the orbit. This can be calculated using the formula:
U = -∫∞r F.dr
where U is the potential energy, F is the electrostatic force, and r is the distance between the electron and the nucleus.
Integrating the above expression, we get:
U = (-1/4πε0) * (eZe/r)
Therefore, the potential energy of the electron in a circular orbit of radius r around a nucleus of charge Ze is given by:
U = - (1/4πε0) * (eZe/r)
which is option B.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer?
Question Description
When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer?.
When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer?.
Solutions for When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice When an electron of charge e and mass m moves with a velocity v about the nuclear charge Ze is circular orbit of radius r, the potential energy of the electrons is given by [1994]a)Ze2/rb)-Ze2/rc)Ze-2/rd)mv2/rCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup