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An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2ħ. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.
(Given: Bohr magneton = 9.274 x 10-24 J/T; ħ = 1.055 x 10-34 J s; electron charge = 1.602 x 10-19 C)
- a)μ = -3.7 x 10-22 J/T, ΔE (Δmj = 2) =1.855 x 10-24 J.
- b)μ = -3.7 x 10-22 J/T, ΔE (Δmj = 1) =1.855 x 10-24 J.
- c)μ = -3.7 x 10-23 J/T, ΔE (Δmj = 1) = 9.274 x 10-25 J.
- d)μ = -3.7 x 10-23 J/T, ΔE (Δmj = 2) = 9.274 x 10-25 J.
Correct answer is option 'C'. Can you explain this answer?
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An electron is moving in a circular orbit of radius 0.5 Å around...
The Zeeman effect describes the splitting of energy levels in atoms in the presence of a magnetic field. The energy splitting is given by:
ΔE = μBΔmjB
where ΔE is the energy splitting, μB is the Bohr magneton, and Δmj is the difference in the magnetic quantum number (Jz) between the two levels.
Here, we are given the radius of the electron's circular orbit, its spin and orbital angular momentum, and the strength of the magnetic field.
From these, we can calculate the magnetic dipole moment (μ) of the electron, which is given by:
μ = -g(μB/ħ) J
where g is the Landé g-factor, which is equal to 2 for a free electron.
Using the given values in the question, we have:
μ = -2(9.274 x 10-24 J/T)/ ħ* 2ħ,
μ = -3.7 x 10-23 J/T.
Next, we can calculate the energy splitting between the two levels.
Since the electron has both spin and orbital angular momentum, we need to consider the total angular momentum of the electron, J = L + S.
The magnetic quantum number Jz can take on values from -J to +J, so the energy splitting will depend on the difference between these values.
For the 3P state, the possible values of J are 1/2 and 3/2, so we need to consider the Δmj values of 1 and 2.
We can calculate the energy splitting for each case as follows:
ΔE (Δmj = 1) = μB(1) B = 9.274 x 10-24 J/T * 0.1 T = 9.274 x 10-25 J,
ΔE (ΔmJ = 2) = μB(2)B = 2(9.274 x 10-24 J/T) * 0.1 T = 1.855 x 10-24 J.
Therefore, the energy splitting due to the Zeeman effect is 9.274 x 10-25 J for Δmj = 1 and 1.855 x 10-24 J for Δmj = 2.
ΔE = μBΔmjB
where ΔE is the energy splitting, μB is the Bohr magneton, and Δmj is the difference in the magnetic quantum number (Jz) between the two levels.
Here, we are given the radius of the electron's circular orbit, its spin and orbital angular momentum, and the strength of the magnetic field.
From these, we can calculate the magnetic dipole moment (μ) of the electron, which is given by:
μ = -g(μB/ħ) J
where g is the Landé g-factor, which is equal to 2 for a free electron.
Using the given values in the question, we have:
μ = -2(9.274 x 10-24 J/T)/ ħ* 2ħ,
μ = -3.7 x 10-23 J/T.
Next, we can calculate the energy splitting between the two levels.
Since the electron has both spin and orbital angular momentum, we need to consider the total angular momentum of the electron, J = L + S.
The magnetic quantum number Jz can take on values from -J to +J, so the energy splitting will depend on the difference between these values.
For the 3P state, the possible values of J are 1/2 and 3/2, so we need to consider the Δmj values of 1 and 2.
We can calculate the energy splitting for each case as follows:
ΔE (Δmj = 1) = μB(1) B = 9.274 x 10-24 J/T * 0.1 T = 9.274 x 10-25 J,
ΔE (ΔmJ = 2) = μB(2)B = 2(9.274 x 10-24 J/T) * 0.1 T = 1.855 x 10-24 J.
Therefore, the energy splitting due to the Zeeman effect is 9.274 x 10-25 J for Δmj = 1 and 1.855 x 10-24 J for Δmj = 2.
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An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer?
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An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer?.
An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer?.
Solutions for An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for UGC NET.
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Here you can find the meaning of An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An electron is moving in a circular orbit of radius 0.5 Å around a nucleus. The electron in the 3p state has a spin of 1/2 and an orbital angular momentum of 2. The atom is placed in a magnetic field of 0.1 T. Determine the splitting of the energy levels and dipole moment due to the Zeeman effect.(Given: Bohr magneton = 9.274 x 10-24J/T; = 1.055 x 10-34J s; electron charge = 1.602 x 10-19C)a)μ = -3.7x 10-22J/T,ΔE(Δmj= 2) =1.855x 10-24J.b)μ = -3.7x 10-22J/T,ΔE(Δmj=1) =1.855x 10-24J.c)μ = -3.7x 10-23J/T,ΔE(Δmj=1) =9.274 x 10-25J.d)μ = -3.7x 10-23J/T,ΔE(Δmj= 2) =9.274 x 10-25J.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice UGC NET tests.
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