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प्रश्न
An α-particle and a proton are released from the centre of the cyclotron and made to accelerate.
(i) Can both be accelerated at the same cyclotron frequency?
Give reason to justify your answer.
(ii) When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the does?
उत्तर
(i) Let us consider: Mass of proton = m, Charge of proton = q, Mass of alpha particle = 4m
Charge of alpha particle = 2q
Cyclotron frequency, `v =(Bq)/(2pim) => v∝q/m`
For proton : Frequency , `v_p∝q/m `
For alpha particle: Frequency ,`v_a ∝(2q)/(4m) or v_a∝q/(2m)`
Thus, particles will not accelerate with same cyclotron frequency. The frequency of proton is twice than the frequency of alpha particle.
(ii)
Velocity,`v =(Bqr)/m =>v∝q/m`
for proton:Velocity, `v_p∝q/m`
For alpha particle : Velocity ,`v_a ∝(2q)/(4m) or v_a∝q/(2m)`
Thus particles will not exit the dees with same velocity. The velocity of proton is twice than the velocity of alpha particle.
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संबंधित प्रश्न
Draw a neat labelled diagram for the construction of 'cyclotron'
Which one of the following particles cannot be accelerated by a cyclotron?
(A) Electrons
(B) Protons
(C) Deuterons
(D) α- particles
Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.
If a charged particle kept at rest experiences an electromagnetic force,
(a) there must be an electric field
(b) there must be a magnetic field
(c) both fields cannot be zero
(d) both fields can be non-zero
Consider a 10-cm long portion of a straight wire carrying a current of 10 A placed in a magnetic field of 0.1 T making an angle of 53° with the wire. What magnetic force does the wire experience?
A conducting wire of length l, lying normal to a magnetic field B, moves with a velocity v,as shown in the figure. (a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end, resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?
(a) An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T. What would be its speed? Is it reasonable? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed?
Cyclotron frequency of a charged particle having charge q and mass m in a cyclotron producing magnetic field B is ______.
Assertion: The frequency of circular motion of a charged particle in cyclotron is independent of the mass of the particle.
Reason: Greater the mass of the particle less will be the frequency of the particle.
A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the ratio frequency field is doubled?
