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  • If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ---------. <img alt="\left [ m_{p}= 1\cdot 67\t

If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ---------.
\left [ m_{p}= 1\cdot 67\times 10^{-27}kg,e= 1\cdot 6\times 10^{-19C},Speed\: of\: light= 3\times 10^{8} m/s \right ]
 

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\Delta \, V= 12\, kV= 12000 \, V
KE of proton is accelerated twice in a cycle
\therefore In each cycle, the KE incresed = 2q\left ( \Delta v \right )
After \, N\, cycle,\, the\, KE \, of \: proton\: will\, be = N\left ( 2q \right )\left ( \Delta \, v \right )= \frac{1}{2}m\, v^{2}
N\left ( 2\times 1\cdot 6\times 10^{-19} \times 12000\right )= \frac{1}{2}\left ( 1\cdot 67\times 10^{-27} \right )\left ( \frac{3\times 10^{8}}{6} \right )^{2}
N= 543\cdot 4
The minimum no of revolution is 543
 

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vishal kumar

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