Question

The maximum energy of a deuteron coming out a cyclotron is $20MeV$. The maximum energy of proton that can be obtained from this accelerator is:

• A. $10MeV$
• B. $20MeV$
• C. $30MeV$
• D. $40MeV$

Answer 1

The correct option is D $40MeV$

In cyclotron output energy of particles coming out for deutron is

$E_d=\frac{q^2{B}^2{R}^2}{2m_D}$

$E_P=\frac{q^2{B}^2{R}^2}{2m_P}$

Taking ratios,

$\frac{E_d}{E_p}=\frac{m_p}{m_d}$$\because m_p=1.6\times {10}^{-27}\&m_d=3.2\times {10}^{-27}$

$\frac{20}{E_P}=\frac{1.6\times {10}^{-27}}{3.2\times {10}^{-27}}$

$E_p=40MeV$