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A proton, a deuteron ion and an alpha-pa...

A proton, a deuteron ion and an `alpha`-particle of equal kinetic energy perform circular motion normal to a uniform magnetic field B. If the radii of their paths are `r_(p),r_(d)andr_(alpha)` respectively then _____ [Here, `q_(d)=q_(p),m_(d)=2m_(p)`]

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we have `r = (mv)/(qB)= (sqrt2mK)/(qB)` Where `K = (1)/(2) mv^2 = kinetic energy.` Thus, `r_p =(sqrt2m,K)/(q_qB), r_d=(sqrt2m_dK)/(q_qB)` and `r_a= (sqrt2m_aK)/(q_aB)` we get `(r_p)/(r_d)= (q_d)/(q_p) sqrt(m_p)/(m_d) =(q_p)/(q_p) sqrt (m_p)/(2m_p)=(1)/sqrt2` and `(rp)/(r_a) =(q_a)/(q_p) sqrt(m_p)/(m_a) = (2q_p)/(q_p) sqrt(m_p)/(4m_p) =1.`
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