
A particle of mass m moves in a circular orbit in a central potential field . If Bohr’s quantization condition is applied, radii of possible orbitals and energy level vary with quantum number as:
A.
B.
C.
D.
Answer
526.5k+ views
1 likes
Hint: In this, we first start by finding the force due to the electric field that is then equate it to the centrifugal force that is which gives us . Then we for the energy we find the total energy as which will give us .
Complete Step-by-Step solution:
Given the potential field in which the particle is moving is
Now we will write the Bohr’s Quantization condition for the allowed state of an electron is
-------------------------- (1)
Where
is the mass which is taken constant
is the velocity of the allowed state
is the orbital radii of the allowed state
is the planck's constant
Now we need to find the relation between and but, we cannot write it directly as is a variable so we need to find how is varying with the .
For that what we will do is that we first found the force due to the electric field using the potential energy expression given in the question that is
--------------------------- (2)
We also know that this force is going to be canceled out by the centrifugal force which is the force exerted on a body due to its motion in a circular path that is
----------------------------- (3)
Now equating equation (2) and (3)
We get
----------------------------- (4)
Where, C is a constant now Substituting (4) in equation (1), we get
Now we find the total energy that is the sum of potential energy which is the energy occupied by the particle due to its height and kinetic energy which is the energy occupied by the particle due to its motion.
------------------------ (5)
Now again substituting (4) in (5) we will get
Hence option D is correct that is
Note: For these types of questions we need to know about different types of forces like force due to electric field, Centrifugal, and centripetal forces. We also need to know about their expression and about Bohr’s law. Coming to energies we need to have a clear understanding of the potential energy and kinetic energies and their expression.
Complete Step-by-Step solution:
Given the potential field in which the particle is moving is
Now we will write the Bohr’s Quantization condition for the allowed state of an electron is
Where
Now we need to find the relation between
For that what we will do is that we first found the force due to the electric field using the potential energy expression given in the question that is
We also know that this force is going to be canceled out by the centrifugal force which is the force exerted on a body due to its motion in a circular path that is
Now equating equation (2) and (3)
We get
Where, C is a constant now Substituting (4) in equation (1), we get
Now we find the total energy
Now again substituting (4) in (5) we will get
Hence option D is correct that is
Note: For these types of questions we need to know about different types of forces like force due to electric field, Centrifugal, and centripetal forces. We also need to know about their expression and about Bohr’s law. Coming to energies we need to have a clear understanding of the potential energy and kinetic energies and their expression.
Recently Updated Pages
Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Chemistry: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Trending doubts
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Gautam Buddha was born in the year A581 BC B563 BC class 10 social science CBSE

Which one is a true fish A Jellyfish B Starfish C Dogfish class 10 biology CBSE

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

What is the median of the first 10 natural numbers class 10 maths CBSE
