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In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.?
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In an hydrogen atom , an electron of mass m and charge e revoloves in ...
The charge crossing any point of the path per second, is n times the charge e of the electron. This constitutes the current round the orbit, i.e. 1=ne. If A 1 the area of the orbit, the magnetic moment is given by the product IA = ne πr^2
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In an hydrogen atom , an electron of mass m and charge e revoloves in ...
Magnetic Moment of an Electron in a Hydrogen Atom
In a hydrogen atom, the electron revolves around the nucleus in an orbit. This orbital motion of the electron generates a magnetic moment. Let's calculate the magnetic moment associated with the orbital motion of the electron.
1. Magnetic Moment Formula
The magnetic moment (μ) associated with the orbital motion of the electron can be calculated using the formula:
μ = - (e/2m) * L
Where:
- μ is the magnetic moment
- e is the charge of the electron
- m is the mass of the electron
- L is the angular momentum of the electron
2. Angular Momentum of the Electron
The angular momentum (L) of the electron can be calculated using the formula:
L = mvr
Where:
- L is the angular momentum
- m is the mass of the electron
- v is the velocity of the electron
- r is the radius of the orbit
3. Velocity of the Electron
The velocity (v) of the electron can be calculated using the formula:
v = 2πrn
Where:
- v is the velocity
- r is the radius of the orbit
- n is the number of revolutions per second
4. Substituting the Values
Now, let's substitute the value of the velocity (v) in the formula for angular momentum (L):
L = m * (2πrn) * r
= 2πmr²n
5. Substituting the Values in Magnetic Moment Formula
Substituting the value of angular momentum (L) in the magnetic moment formula:
μ = - (e/2m) * (2πmr²n)
= - (e/2m) * (4πmnr²)
Simplifying further:
μ = - (2πe/m) * (nr²)
6. Magnetic Moment of the Electron
Therefore, the magnetic moment (μ) associated with the orbital motion of the electron in a hydrogen atom is given by:
μ = - (2πe/m) * (nr²)
This equation represents the magnetic moment of the electron in the hydrogen atom, which is influenced by the mass of the electron, charge of the electron, radius of the orbit, and the number of revolutions per second.
In a hydrogen atom, the electron revolves around the nucleus in an orbit. This orbital motion of the electron generates a magnetic moment. Let's calculate the magnetic moment associated with the orbital motion of the electron.
1. Magnetic Moment Formula
The magnetic moment (μ) associated with the orbital motion of the electron can be calculated using the formula:
μ = - (e/2m) * L
Where:
- μ is the magnetic moment
- e is the charge of the electron
- m is the mass of the electron
- L is the angular momentum of the electron
2. Angular Momentum of the Electron
The angular momentum (L) of the electron can be calculated using the formula:
L = mvr
Where:
- L is the angular momentum
- m is the mass of the electron
- v is the velocity of the electron
- r is the radius of the orbit
3. Velocity of the Electron
The velocity (v) of the electron can be calculated using the formula:
v = 2πrn
Where:
- v is the velocity
- r is the radius of the orbit
- n is the number of revolutions per second
4. Substituting the Values
Now, let's substitute the value of the velocity (v) in the formula for angular momentum (L):
L = m * (2πrn) * r
= 2πmr²n
5. Substituting the Values in Magnetic Moment Formula
Substituting the value of angular momentum (L) in the magnetic moment formula:
μ = - (e/2m) * (2πmr²n)
= - (e/2m) * (4πmnr²)
Simplifying further:
μ = - (2πe/m) * (nr²)
6. Magnetic Moment of the Electron
Therefore, the magnetic moment (μ) associated with the orbital motion of the electron in a hydrogen atom is given by:
μ = - (2πe/m) * (nr²)
This equation represents the magnetic moment of the electron in the hydrogen atom, which is influenced by the mass of the electron, charge of the electron, radius of the orbit, and the number of revolutions per second.
Community Answer
In an hydrogen atom , an electron of mass m and charge e revoloves in ...
Magnetic moment= -emvr/2m
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In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.?
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In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.?.
In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an hydrogen atom , an electron of mass m and charge e revoloves in an orbit of radius r making n revolution per second . if the mass of the hydrogen nucleus is M ,the magnetic moment associated with the orbital motion of electron.?.
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