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An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rα and rs respectively. The ratio rs/rα is ________.
Correct answer is '4'. Can you explain this answer?
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An α -particle (mass 4 amu) and a singly charged sulfur ion (mas...
Given Data:
- Mass of α-particle (mα) = 4 amu
- Mass of singly charged sulfur ion (ms) = 32 amu
- Initial velocities of particles = 0
- Potential difference = V
- Ratio of radii of circular orbits = rs/rα
Concept:
- The kinetic energy gained by the particles due to acceleration through potential V will be converted into their kinetic energy in the magnetic field.
- Kinetic energy of a charged particle in a magnetic field is given by K = qVB, where q is the charge of the particle, V is the potential difference, and B is the magnetic field strength.
Calculation:
- Since the particles are accelerated through the same potential difference, their kinetic energies in the magnetic field will be the same.
- Setting up the equation for both particles:
1. For α-particle: (1/2) mα vα^2 = qVB
2. For sulfur ion: (1/2) ms vs^2 = qVB
- The ratio of the radii of the circular orbits is given by:
rs/rα = (ms vs^2)/(mα vα^2)
- Since both particles have the same kinetic energy in the magnetic field:
mα vα^2 = ms vs^2
Hence, rs/rα = ms/mα = 32/4 = 8/2 = 4
Therefore, the ratio rs/rα is 4.
- Mass of α-particle (mα) = 4 amu
- Mass of singly charged sulfur ion (ms) = 32 amu
- Initial velocities of particles = 0
- Potential difference = V
- Ratio of radii of circular orbits = rs/rα
Concept:
- The kinetic energy gained by the particles due to acceleration through potential V will be converted into their kinetic energy in the magnetic field.
- Kinetic energy of a charged particle in a magnetic field is given by K = qVB, where q is the charge of the particle, V is the potential difference, and B is the magnetic field strength.
Calculation:
- Since the particles are accelerated through the same potential difference, their kinetic energies in the magnetic field will be the same.
- Setting up the equation for both particles:
1. For α-particle: (1/2) mα vα^2 = qVB
2. For sulfur ion: (1/2) ms vs^2 = qVB
- The ratio of the radii of the circular orbits is given by:
rs/rα = (ms vs^2)/(mα vα^2)
- Since both particles have the same kinetic energy in the magnetic field:
mα vα^2 = ms vs^2
Hence, rs/rα = ms/mα = 32/4 = 8/2 = 4
Therefore, the ratio rs/rα is 4.
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An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer?
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An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer?.
An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An α -particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of a uniform magnetic field which is normal to the velocities of the particles. Within this region, the -particle and the sulfur ion move in circular orbits of radii rαand rsrespectively. The ratio rs/rαis ________.Correct answer is '4'. Can you explain this answer?.
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