If the maximum value of accelerating potential provided by a ratio 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 ....... .
$\left[{m}_{{p}}=1.67 \times 10^{-27} {kg}, {e}=1.6 \times 10^{-19} {C},\right.$ Speed of light $\left.=3 \times 10^{8} {m} / {s}\right]$
JEE MAIN 2021, Diffcult
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${V}=12\, {kV}$
Number of revolution $={n}$
${n}\left[2 \times {q}_{{P}} \times {V}\right]=\frac{1}{2} {m}_{{p}} \times {v}_{{P}}^{2}$
${n}\left[2 \times 1.6 \times 10^{-19} \times 12 \times 10^{3}\right.$
$=\frac{1}{2} \times 1.67 \times 10^{-27} \times\left[\frac{3 \times 10^{8}}{6}\right]^{2}$
${n}\left(38.4 \times 10^{-16}\right)=0.2087 \times 10^{-11}$
${n}=543.4$
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