Maximum spatial separation of beams, when the two isotopes have same energies is

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Professor PC Thomas Classes · Answer

(b) : For a charged particle, radius of path 
$ r=\frac{m v}{q B} $
 $ \Rightarrow r=\frac{m v}{q B}=\frac{\sqrt{2 m K}}{B q} $
 When particles (nuclei of 2-different isotopes) have same energies, then 
$ r_1=\frac{\sqrt{2 m_1 K}}{B Z} 	ext { and } r_2=\frac{\sqrt{2 m_2 K}}{B Z} $ 
Separation between two traces, \ $d=2 r_2-2 r_1$\ $=\frac{2 \sqrt{2 m_2 K}}{B Z}-\frac{2 \sqrt{2 m_1 K}}{B Z}=\frac{2 \sqrt{2 K}}{B Z}\left(\sqrt{m_2}-\sqrt{m_1}ight)$