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A cyclotron is device for accelerating i...

A cyclotron is device for accelerating ions and charged particles. It was developed by Lawerence in 1932.
The heart of the appritus consists of a split metal pillbox. Figure sHOws top and front views of the halves called dees. A rapidly oscilating potential difference is applied between the Dees. This produces an oscilating electric field in the gap between the dees, the region inside each dee being essentially free of electric field. The Dees are enclosed in an evaccutaed container, and the entire unit is placed in a uniform magnetic field B whose direction is normal to the plane Of Dees, A charged particle of mass 'm' and charge 'q' in the gap between the dees, it moves with constant speed in a semi-circle.
The period of uniform circular motion is `T=(2pim)/(qB)` and is independant of speed. If the time-period of the oscilating elctric field is equal to this time, then the charged particle will be accelerated again and again

Answer the following questions (consider the mass of particles remains constant during motion):
A cyclotron is accelerating deutrons having mass=`2xx1.6xx10^(-27)` kg and charge +e. If B=2T, then the required angular frequency of oscilating electric field is :

A

`10^(8)` radian`//`sec

B

`10^(7)` radian`//`sec

C

`10^(10)` radian`//`sec

D

`10^(9)` radian`//`sec

Text Solution

Verified by Experts

The correct Answer is:
A
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A cyclotron is device for accelerating ions and charged particles. It was developed by Lawerence in 1932. The heart of the appritus consists of a split metal pillbox. Figure sHOws top and front views of the halves called dees. A rapidly oscilating potential difference is applied between the Dees. This produces an oscilating electric field in the gap between the dees, the region inside each dee being essentially free of electric field. The Dees are enclosed in an evaccutaed container, and the entire unit is placed in a uniform magnetic field B whose direction is normal to the plane Of Dees, A charged particle of mass 'm' and charge 'q' in the gap between the dees, it moves with constant speed in a semi-circle. The period of uniform circular motion is T=(2pim)/(qB) and is independant of speed. If the time-period of the oscilating elctric field is equal to this time, then the charged particle will be accelerated again and again Answer the following questions (consider the mass of particles remains constant during motion): A cyclotron has been adjusted to accelereted deutrons. It is now to be adjusted to accelerate other particles , for this following changes may be made: (a) In order to keep the frequency of oscillating electric field same, the magnetic field is halved for proton (b) If the magnetic field remain unchanged, the oscillation frequency of electric field should be halved for alpha particle (c ) If the magnetic field remain unchanged, the oscillation frequency of electric field should be double for proton (d) If the frequency of oscillating electric field is kept same, the magnetic field should be kept same for alpha particle

A cyclotron is device for accelerating ions and charged particles. It was developed by Lawerence in 1932. The heart of the appritus consists of a split metal pillbox. Figure sHOws top and front views of the halves called dees. A rapidly oscilating potential difference is applied between the Dees. This produces an oscilating electric field in the gap between the dees, the region inside each dee being essentially free of electric field. The Dees are enclosed in an evaccutaed container, and the entire unit is placed in a uniform magnetic field B whose direction is normal to the plane Of Dees, A charged particle of mass 'm' and charge 'q' in the gap between the dees, it moves with constant speed in a semi-circle. The period of uniform circular motion is T=(2pim)/(qB) and is independant of speed. If the time-period of the oscilating elctric field is equal to this time, then the charged particle will be accelerated again and again In a cyclotron resonance experiment, if we assume that maximum radius attained by any chared particles is equal to radius of dees, then minimum kinetics energy gained by the particles will be

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