Advertisements
Advertisements
प्रश्न
A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.
उत्तर
Frequency of oscillators (v) = 10 MHz = 107 Hz
Mass of proton, `"m" = 1.67 xx 10^-27 "kg"`
Charge of proton = 1.6 x 10-19 C
Operating magnetic field is given by the relation
`"B" = (2pi"mv")/q = (2 xx 3.14 xx 1.67 xx 10^-27 xx 10^7)/(1.6 xx 10^-19)`
= 0.65 T
Radius of dees= 60 cm = 0.6 m
`"KE" = ("q"^2"B"^2"r"^2)/(2"m") = ((1.6 xx 10^-19)^2(0.65)^2(0.6)^2)/(2 xx 1.67 xx 10^-27 xx 1.6 xx 10^-13) "Mev"`.
APPEARS IN
संबंधित प्रश्न
State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies
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?
(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?
\[\ce{Fe+}\] ions are accelerated through a potential difference of 500 V and are injected normally into a homogeneous magnetic field B of strength 20.0 mT. Find the radius of the circular paths followed by the isotopes with mass numbers 57 and 58. Take the mass of an ion = A (1.6 × 10−27) kg, where A is the mass number.
Cyclotron frequency of a charged particle having charge q and mass m in a cyclotron producing magnetic field B is ______.
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?
The life time of muon in the rest frame is 2 × 10-6 sec. A beam of muons emerges from a cyclotron with velocity where c is the velocity of light The mean life of muons observed in the laboratory frame will be ______.
In a cyclotron, a charged particle ______.
