Question

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

• A. 40 MeV
• B. 80 MeV
• C. 20 MeV
• D. 160 MeV

Answer 1

The correct option is B 80 MeV

$F=qVB=\frac{m{v}^2}{r}$

$E=\frac{1}{2}\frac{B^2{q}^2{r}^2}{m}$

Hence ratio of energy of deuteron and proton

$\frac{E_d}{E_p}=\left(\frac{q_d}{q_p}\right)\left(\frac{M_p}{M_d}\right)\left(\frac{40}{E_p}\right)=\left(\frac{q}{q}{)}^2\right(\frac{m}{2m})=(\frac{1}{2})$

$E_P=2Ed$

$=2\times 40MeV$

$=80MeV$

Hence (B) option is correct