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  • Oscillating frequency of a cyclotron is 10MHz. if the radius of its Dees is 0.5m,Then K.E of a proton which is accelarated by the cyclotron isOption: 1

Oscillating frequency of a cyclotron is 10MHz. if the radius of its Dees is 0.5m,Then K.E of a proton which is accelarated by the cyclotron is

Option: 1

10.2MeV


Option: 2

2.55MeV


Option: 3

5.1MeV


Option: 4

1.5MeV


Answers (1)

The maximum energy of a particle in a cyclotron -

KE of charged possible in a cyclotron, E_{k}=\frac{q^{2} B^{2} r^{2}}{2 m}
But frequency f=\frac{q B}{2 \pi m}
\begin{aligned} \\ E_{k}=\frac{(2 \pi m f)^{2} r^{2}}{2 m}=2 \pi^{2} m f^{2} r^{2} \\ E_{k}=2 \times(3.14)^{2} \times 1.67 \times 10^{-27} \times\left(10 \times 10^{6}\right)^{2} \times (0.5)^2 \\ \therefore E_{k}=\frac{8.23 \times 10^{-13}}{1.6 \times 10^{-19}}=5.1 \times 10^{6} \mathrm{eV}=5.1 \mathrm{MeV} \end{aligned}

 

Posted by

Sumit Saini

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