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Suppose an electron is attracted towards the origin by a force k/r where 'k' is a constant and 'r' is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be 'r'n and the kinetic energy of the electron to be Tn . Then which of the following is true ?
- a)Tn ∝ 1 ∕ n2 , rn ∝ n2
- b)Tn independent of n , rn ∝ n
- c)Tn ∝ 1 ∕ n , rn ∝ n
- d)Tn ∝ 1 ∕ n ,rn ∝ n2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Suppose an electron is attracted towards the origin by a force k/r whe...
Since we are applying the Bohr model, we can assume that the electron is in a circular orbit around the origin. The electrostatic force between the electron and the origin is given by Coulomb's law:
F = kq1q2/r^2
where q1 and q2 are the charges of the electron and the origin, respectively. Since the electron has a negative charge and the origin has a positive charge, the force is attractive.
We can equate this force to the centripetal force required to keep the electron in a circular orbit:
F = mv^2/r
where m is the mass of the electron and v is its velocity.
Substituting the force expression in terms of k and r, we get:
kq1q2/r^2 = mv^2/r
Simplifying and rearranging, we get:
v = sqrt(kq1q2/mr)
The angular momentum of the electron in this orbit is given by:
L = mvr
The quantization condition for the angular momentum in the Bohr model is:
L = nħ
where n is a positive integer (the quantum number) and ħ is the reduced Planck constant.
Substituting the expressions for v and L, we get:
mvr = nħ
mr^2 = n^2ħ^2/kq1q2
The potential energy of the electron in this system is given by:
U = -kq1q2/r
The total energy of the electron in the nth orbit is the sum of its kinetic and potential energies:
E = Tn + U = Tn - kq1q2/rn
Since the electron is assumed to be in a circular orbit, its kinetic energy can be expressed in terms of its momentum p as:
Tn = p^2/2m
Substituting the expressions for p and rn from the above equations, we get:
Tn = (n^2ħ^2/kq1q2)(1/2m)
The given expression for the force is similar to the Coulomb force between a positive and negative charge, except that the force constant k is not equal to the Coulomb constant 1/4πε0. However, this does not affect the derivation of the Bohr model, since the equations are still valid as long as the force is central (i.e., depends only on the distance from the origin) and inverse square.
Therefore, the correct statement is:
a) Tn < 0="" for="" all="" n="" 0="" for="" all="" />
F = kq1q2/r^2
where q1 and q2 are the charges of the electron and the origin, respectively. Since the electron has a negative charge and the origin has a positive charge, the force is attractive.
We can equate this force to the centripetal force required to keep the electron in a circular orbit:
F = mv^2/r
where m is the mass of the electron and v is its velocity.
Substituting the force expression in terms of k and r, we get:
kq1q2/r^2 = mv^2/r
Simplifying and rearranging, we get:
v = sqrt(kq1q2/mr)
The angular momentum of the electron in this orbit is given by:
L = mvr
The quantization condition for the angular momentum in the Bohr model is:
L = nħ
where n is a positive integer (the quantum number) and ħ is the reduced Planck constant.
Substituting the expressions for v and L, we get:
mvr = nħ
mr^2 = n^2ħ^2/kq1q2
The potential energy of the electron in this system is given by:
U = -kq1q2/r
The total energy of the electron in the nth orbit is the sum of its kinetic and potential energies:
E = Tn + U = Tn - kq1q2/rn
Since the electron is assumed to be in a circular orbit, its kinetic energy can be expressed in terms of its momentum p as:
Tn = p^2/2m
Substituting the expressions for p and rn from the above equations, we get:
Tn = (n^2ħ^2/kq1q2)(1/2m)
The given expression for the force is similar to the Coulomb force between a positive and negative charge, except that the force constant k is not equal to the Coulomb constant 1/4πε0. However, this does not affect the derivation of the Bohr model, since the equations are still valid as long as the force is central (i.e., depends only on the distance from the origin) and inverse square.
Therefore, the correct statement is:
a) Tn < 0="" for="" all="" n="" 0="" for="" all="" />
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Community Answer
Suppose an electron is attracted towards the origin by a force k/r whe...
We cannot determine whether Tn is positive or negative without additional information about the state of the electron. However, we can make the following statements based on the given information:
b) The potential energy of the electron in the nth orbital is proportional to 1/rn. This is because the potential energy is given by -k/r, and in the Bohr model, the electron is assumed to be in a circular orbit at a fixed distance from the origin. Thus, the potential energy is inversely proportional to the distance, or 1/rn.
c) The total energy of the electron in the nth orbital is given by En = Tn - k/rn. This is because the total energy is the sum of the kinetic and potential energies, and we know that the potential energy is -k/rn (as stated in part b)).
d) The energy of the electron in the nth orbital is quantized, meaning it can only take on certain discrete values. This is a fundamental postulate of the Bohr model. The energy is given by En = -13.6 eV/n^2, where n is the principal quantum number (the integer value of the orbital). Therefore, we can write:
Tn - k/rn = -13.6 eV/n^2
or
Tn = k/rn - 13.6 eV/n^2
This shows that the kinetic energy of the electron in the nth orbital is related to the radius of the orbit and the principal quantum number.
b) The potential energy of the electron in the nth orbital is proportional to 1/rn. This is because the potential energy is given by -k/r, and in the Bohr model, the electron is assumed to be in a circular orbit at a fixed distance from the origin. Thus, the potential energy is inversely proportional to the distance, or 1/rn.
c) The total energy of the electron in the nth orbital is given by En = Tn - k/rn. This is because the total energy is the sum of the kinetic and potential energies, and we know that the potential energy is -k/rn (as stated in part b)).
d) The energy of the electron in the nth orbital is quantized, meaning it can only take on certain discrete values. This is a fundamental postulate of the Bohr model. The energy is given by En = -13.6 eV/n^2, where n is the principal quantum number (the integer value of the orbital). Therefore, we can write:
Tn - k/rn = -13.6 eV/n^2
or
Tn = k/rn - 13.6 eV/n^2
This shows that the kinetic energy of the electron in the nth orbital is related to the radius of the orbit and the principal quantum number.
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Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer?.
Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer?.
Solutions for Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Suppose an electron is attracted towards the origin by a force k/r where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn . Then which of the following is true ?a)Tn∝ 1 n2, rn ∝ n2b)Tn independent of n , rn ∝ nc)Tn ∝ 1 n , rn ∝ nd)Tn ∝ 1 n ,rn ∝ n2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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