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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.
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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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