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A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?
- a)1 MeV
- b)2 MeV
- c)4 MeV
- d)0.5 MeV
Correct answer is option 'A'. Can you explain this answer?
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A proton of mass m and charge +e is moving in a circular orbit in a m...
Here ‘r’ and ‘ B’ are constants
∴ 
∴ 
⇒ Kα = 1 MeV.
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A proton of mass m and charge +e is moving in a circular orbit in a m...
Given data:
Mass of proton (m) = m
Charge of proton (e) = e
Mass of alpha particle (4m)
Charge of alpha particle (2e)
Energy of proton in circular orbit (E) = 1 MeV
Concept:
The energy of a charged particle in a magnetic field is given by the equation:
E = B^2 * r^2 * m / 2q
where E is the energy, B is the magnetic field, r is the radius of the circular orbit, m is the mass of the particle, and q is the charge of the particle.
Solution:
To find the energy of the alpha particle (E'), we need to equate the energy equation for the proton and the alpha particle.
For proton:
E = B^2 * r^2 * m / 2e
For alpha particle:
E' = B^2 * r^2 * (4m) / 4e
Step 1: Simplify the equation for the alpha particle's energy:
E' = B^2 * r^2 * m / e
Step 2: Substitute the value of E from the given data:
1 MeV = B^2 * r^2 * m / 2e
Step 3: Substitute the value of E' from Step 1 into the equation:
1 MeV = B^2 * r^2 * m / e
Step 4: Simplify the equation:
1 MeV = B^2 * r^2 * m / e
Multiplying both sides of the equation by 2:
2 MeV = B^2 * r^2 * m / e
Step 5: Divide both sides of the equation by 2:
1 MeV = B^2 * r^2 * m / 2e
This equation is the same as the energy equation for the proton. Therefore, the energy of the alpha particle in a circular orbit of the same radius in the same magnetic field is 1 MeV, which is option A.
Mass of proton (m) = m
Charge of proton (e) = e
Mass of alpha particle (4m)
Charge of alpha particle (2e)
Energy of proton in circular orbit (E) = 1 MeV
Concept:
The energy of a charged particle in a magnetic field is given by the equation:
E = B^2 * r^2 * m / 2q
where E is the energy, B is the magnetic field, r is the radius of the circular orbit, m is the mass of the particle, and q is the charge of the particle.
Solution:
To find the energy of the alpha particle (E'), we need to equate the energy equation for the proton and the alpha particle.
For proton:
E = B^2 * r^2 * m / 2e
For alpha particle:
E' = B^2 * r^2 * (4m) / 4e
Step 1: Simplify the equation for the alpha particle's energy:
E' = B^2 * r^2 * m / e
Step 2: Substitute the value of E from the given data:
1 MeV = B^2 * r^2 * m / 2e
Step 3: Substitute the value of E' from Step 1 into the equation:
1 MeV = B^2 * r^2 * m / e
Step 4: Simplify the equation:
1 MeV = B^2 * r^2 * m / e
Multiplying both sides of the equation by 2:
2 MeV = B^2 * r^2 * m / e
Step 5: Divide both sides of the equation by 2:
1 MeV = B^2 * r^2 * m / 2e
This equation is the same as the energy equation for the proton. Therefore, the energy of the alpha particle in a circular orbit of the same radius in the same magnetic field is 1 MeV, which is option A.
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A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer?
Question Description
A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer?.
A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A proton of mass m and charge +e is moving in a circular orbit in a magnetic field with energy 1 MeV. What should be the energy of an α - particle (mass 4m and charge +2e) so that it revolves in a circular orbit of the same radius in the same magnetic field?a)1 MeVb)2 MeVc)4 MeVd)0.5 MeVCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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