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CBSE Class 12-science Answered

A proton and a deuteron having the same kinetic energies enter region of uniform magnetic field perpendicularly. Deuteron's mass is twice that of proton. Calculate the ratio of the radii of their circular paths.
Asked by Jamil.4579 | 09 Aug, 2019, 01:13: PM
answered-by-expert Expert Answer
Force F experienced by a charge particle moving vith speed v, having mass m and charge q is given by,
 
F = B×q×v = (1/2)mv2/R    .........................(1)
 
RHS of eqn.(1) is centripetal force and R is radius of circular path.
 
Hence from eqn.(1), we get radius R = B×q/(m×v) .....................(2)
 
if we use kinetic energy E = (1/2) mv2 in eqn.(2),  then Radius R = ( B×q ) / (2×m×E)1/2  .....................(3)
 
Hence for a given charge q,  given kinetic energy and magnetic induction B, Radius R begin mathsize 14px style proportional to end style (1/√m)    ................(4)
 
Since proton and deutron have same charge but mass of deutron is twice of that of proton,
if RP is radius of proton and RD is radius of deutron,
 
then  begin mathsize 14px style R subscript P over R subscript D space equals space square root of m subscript D over m subscript P space end root space equals space square root of 2 end style
Answered by Thiyagarajan K | 09 Aug, 2019, 02:28: PM

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