In a cyclotron, if a deuteron can gain an energy of 40 MeV, then a proton can gain an energy of

Options

A. `40 MeV`
B. `80 MeV`
C. `20 MeV`
D. `60 MeV`

Answer

B

Explanation

In a cyclotron,`R=(mv)/(qB)=sqrt(2Km)/(qB)`where K is the K.E of the revoloving particle. `therefore sqrt(2Km)=qBR` Now charge on the proton=charge on the deutron and B and R are kept fixed.`thereforesqrt(2mK)=`constant therefre 2mK=constant or `Kpropto1/m therefore (k_p)/K_d=m_d/m_p=2/1 therefore K_p=2K_d=2 xx 40 =80 MeV`.