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Protons are accelerated in a cyclotron w...

Protons are accelerated in a cyclotron where the appilied magnetic field is 2T and the P.D across the dees is 100 KV. How many revolutions the protons has to complete to acquire a K.E. MeV?

A

`50`

B

`100`

C

`150`

D

`200`

Text Solution

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The correct Answer is:
To solve the problem of how many revolutions protons must complete in a cyclotron to acquire a kinetic energy of 20 MeV, we can follow these steps: ### Step 1: Understand the relationship between potential difference and kinetic energy In a cyclotron, when a charged particle (like a proton) is accelerated through a potential difference (P.D.), it gains kinetic energy (K.E.). The kinetic energy gained by a charged particle can be calculated using the formula: \[ K.E. = q \cdot V \] where \( q \) is the charge of the particle and \( V \) is the potential difference. ### Step 2: Calculate the charge of a proton The charge of a proton (\( q \)) is approximately: \[ q = 1.6 \times 10^{-19} \text{ C} \] ### Step 3: Convert the potential difference to joules Given that the potential difference across the dees is 100 kV, we convert this to volts: \[ V = 100 \times 10^3 \text{ V} = 100,000 \text{ V} \] ### Step 4: Calculate the kinetic energy gained after one revolution Now, we can calculate the kinetic energy gained after one complete revolution: \[ K.E. = q \cdot V = (1.6 \times 10^{-19} \text{ C}) \cdot (100,000 \text{ V}) = 1.6 \times 10^{-14} \text{ J} \] ### Step 5: Convert kinetic energy from joules to MeV To convert joules to MeV, we use the conversion factor \( 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \): \[ K.E. = \frac{1.6 \times 10^{-14} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} = 10^5 \text{ eV} = 0.1 \text{ MeV} \] ### Step 6: Determine the number of revolutions needed for 20 MeV Now, we need to find out how many revolutions are required to achieve a kinetic energy of 20 MeV: \[ \text{Number of revolutions} = \frac{\text{Total K.E. desired}}{\text{K.E. gained per revolution}} = \frac{20 \text{ MeV}}{0.1 \text{ MeV}} = 200 \] ### Conclusion Thus, the protons must complete **200 revolutions** to acquire a kinetic energy of 20 MeV.
To solve the problem of how many revolutions protons must complete in a cyclotron to acquire a kinetic energy of 20 MeV, we can follow these steps: ### Step 1: Understand the relationship between potential difference and kinetic energy In a cyclotron, when a charged particle (like a proton) is accelerated through a potential difference (P.D.), it gains kinetic energy (K.E.). The kinetic energy gained by a charged particle can be calculated using the formula: \[ K.E. = q \cdot V \] where \( q \) is the charge of the particle and \( V \) is the potential difference. ...
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Protons are accelerated in a cyclotron using a magnetic field of 1.3 T. Calculate the frequency with which the electric field between the dees should be reversed.

Protons are accelerated in a cyclotron so that the maximum curvature radius of their trajectory is equal to r = 50 cm . Find: (a) the kinetic energy of the protons when the acceleration is completed if the magnetic induction in the cyclotron is B = 1.0 T , (b) the minimum frequency of the cycloroton's oscillator at which the kinetic energy of the protons amounts to T = 20 Me V by the end of accelearation.

Knowledge Check

  • The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. Cyclotron is not suitable for accelerating

    A
    Electron
    B
    Protons
    C
    Deutrons
    D
    Alpha particles

  • The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. Which of the following cannot be accelerated in a cyclotron?

    A
    Protons
    B
    Deutrons
    C
    Alpha particles
    D
    Neutrons

  • The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. The working of a cyclotron is based on the fact that

    A
    The force experienced by a charged particles in an electric field is independent of its velocity
    B
    The radius of the circular orbit of a charged particle in a magnetic field increase with increase in its speed
    C
    The frequency of revolution of the particle along the circular path does not depend on its speed
    D
    All of the above

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