A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........

Pick an option to check your answer.

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Answer & Solution

Correct Answer

(A) \(2\)

Detailed explanation

\(R =\frac{ mv }{ q _{ B }}\)

\(R _{ D }=\frac{\left(2 m _{ p }\right) v _{ D }}{ e B}\)

\(R _{ p }=\frac{\left( m _{ p }\right) v _{ p }}{ e B }\)

\(\frac{ R _{ D }}{ R _{ p }}=\frac{2 v _{ D }}{ v _{ p }}=\frac{2 v _{ D }}{\sqrt{2} v _{ D }}=\frac{\sqrt{2}}{1}\)

\(\frac{1}{2}\left(2 mp _{ D }\right) v _{ D }^{2}=\frac{1}{2} m _{ p } \cdot v _{ p }^{2}\)

\(\sqrt{2} v _{ D }= v _{ p }\)

\(x =2\)

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